class: center, middle, inverse, title-slide # APSTA-GE 2003: Intermediate Quantitative Methods ## Lab Section 003, Week 8 ### New York University ### 10/27/2020 --- ## Reminders - **Assignment 4** - Due: **10/28/2020 11:55pm (EST)** - Updated Shiny App: [https://tongj.shinyapps.io/2003iqm](https://tongj.shinyapps.io/2003iqm) - **Assignment 5** - Due: **11/06/2020 11:55pm (EST)** - Office hours - Monday 9 - 10am (EST) - Wednesday 12:30 - 1:30pm (EST) - Additional time slots available - Sign-up sheet [HERE](https://docs.google.com/spreadsheets/d/1YY38yj8uCNIm1E7jaI9TJC494Pye2-Blq9eSK_eh6tI/edit?usp=sharing) - Office hour Zoom link - https://nyu.zoom.us/j/97347070628 (pin: 2003) - Office hour notes - Available on NYU Classes --- ## Today's Topics - Review on Multiple Regression - Multiple Regression Analysis --- class: inverse, center, middle # Review on Multiple Regression --- ## Multiple Regression - Linear: straight line `$$Y_i = X_i + \varepsilon$$` - Multiple linear regression: - A linear regression with two or more independent variables - Types of multiple linear regression: - Additive - Interaction --- ## Additive **Additive model equation: ** `$$Y_i = \beta_0 + \beta_1 \cdot X_{i1} + \beta_2 \cdot X_{i2} + ... + \beta_n \cdot X_{ik} + \varepsilon_i, \ \ \ i = 1, ..., n$$` It can also be written as: `$$\mathcal{Y_i} = \beta_0 + \mathcal{X} + \varepsilon_i$$` `$$\mathcal{X} = \beta_1 \cdot X_{i1} + \beta_2 \cdot X_{i2} + ... + \beta_n \cdot X_{ik}$$` This reveals an additive relation: - slopes are independent - regression lines are parallel --- ## Demo 1: Additive ```r dat1 <- read.csv("lung_capacity0.csv") dplyr::glimpse(dat1) ``` ``` ## Observations: 80 ## Variables: 6 ## $ Sex <int> 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, … ## $ Height <dbl> 66.9, 67.1, 70.7, 70.9, 73.3, 76.1, 70.9, 71.9, 71.1, … ## $ Smoker <int> 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, … ## $ Exercise <int> 22, 23, 21, 18, 31, 39, 26, 0, 18, 22, 19, 22, 15, 1, … ## $ Age <int> 49, 41, 82, 26, 69, 42, 68, 40, 35, 50, 40, 58, 19, 33… ## $ LungCapacitycc <int> 5093, 5116, 5550, 5530, 5929, 6212, 5723, 5133, 5415, … ``` ```r summary(mod1 <- lm(LungCapacitycc ~ Age + Smoker, data = dat1))$coefficients ``` ``` ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 5455.194065 131.083801 41.6160808 1.534390e-54 ## Age 2.004431 2.532095 0.7916099 4.310200e-01 ## Smoker -596.342602 68.393054 -8.7193446 4.169716e-13 ``` `$$\text{Lung Capacity} = 5455.194 + 2.004 \cdot \text{Age} - 596.343 \cdot \text{Smoker} + \varepsilon$$` --- ## Demo 1: Additive (Continued) ```r summary(mod1)$coefficients["Smoker", ] ``` ``` ## Estimate Std. Error t value Pr(>|t|) ## -5.963426e+02 6.839305e+01 -8.719345e+00 4.169716e-13 ``` <div id="htmlwidget-2bb5311923f045e5d9de" style="width:720px;height:432px;" class="plotly html-widget"></div> <script type="application/json" data-for="htmlwidget-2bb5311923f045e5d9de">{"x":{"data":[{"x":[49,41,82,26,69,42,68,50,58,59,39,36,67,58,65,40,36,73,45,32,28,32,28,42,69,45,69,32,45,54,45,32,50,42,41,67,44,35,38,43,71,66,35,47],"y":[5093,5116,5550,5530,5929,6212,5723,5075,5072,5285,6261,5712,5547,5557,5551,5122,5531,5187,5657,5655,5010,5625,5156,5278,5793,5625,5760,5594,5402,5843,5692,5484,5776,5770,5764,5632,5585,5683,5734,5187,5518,5959,5400,5673],"text":["Age: 49<br />LungCapacitycc: 5093<br />Smoker: 0","Age: 41<br />LungCapacitycc: 5116<br />Smoker: 0","Age: 82<br />LungCapacitycc: 5550<br />Smoker: 0","Age: 26<br />LungCapacitycc: 5530<br />Smoker: 0","Age: 69<br />LungCapacitycc: 5929<br />Smoker: 0","Age: 42<br />LungCapacitycc: 6212<br />Smoker: 0","Age: 68<br />LungCapacitycc: 5723<br />Smoker: 0","Age: 50<br />LungCapacitycc: 5075<br />Smoker: 0","Age: 58<br />LungCapacitycc: 5072<br />Smoker: 0","Age: 59<br />LungCapacitycc: 5285<br />Smoker: 0","Age: 39<br />LungCapacitycc: 6261<br />Smoker: 0","Age: 36<br />LungCapacitycc: 5712<br />Smoker: 0","Age: 67<br />LungCapacitycc: 5547<br />Smoker: 0","Age: 58<br />LungCapacitycc: 5557<br />Smoker: 0","Age: 65<br />LungCapacitycc: 5551<br />Smoker: 0","Age: 40<br />LungCapacitycc: 5122<br />Smoker: 0","Age: 36<br />LungCapacitycc: 5531<br />Smoker: 0","Age: 73<br />LungCapacitycc: 5187<br />Smoker: 0","Age: 45<br />LungCapacitycc: 5657<br />Smoker: 0","Age: 32<br />LungCapacitycc: 5655<br />Smoker: 0","Age: 28<br />LungCapacitycc: 5010<br />Smoker: 0","Age: 32<br />LungCapacitycc: 5625<br />Smoker: 0","Age: 28<br />LungCapacitycc: 5156<br />Smoker: 0","Age: 42<br />LungCapacitycc: 5278<br />Smoker: 0","Age: 69<br />LungCapacitycc: 5793<br />Smoker: 0","Age: 45<br />LungCapacitycc: 5625<br />Smoker: 0","Age: 69<br />LungCapacitycc: 5760<br />Smoker: 0","Age: 32<br />LungCapacitycc: 5594<br />Smoker: 0","Age: 45<br />LungCapacitycc: 5402<br />Smoker: 0","Age: 54<br />LungCapacitycc: 5843<br />Smoker: 0","Age: 45<br />LungCapacitycc: 5692<br />Smoker: 0","Age: 32<br />LungCapacitycc: 5484<br />Smoker: 0","Age: 50<br />LungCapacitycc: 5776<br />Smoker: 0","Age: 42<br />LungCapacitycc: 5770<br />Smoker: 0","Age: 41<br />LungCapacitycc: 5764<br />Smoker: 0","Age: 67<br />LungCapacitycc: 5632<br />Smoker: 0","Age: 44<br />LungCapacitycc: 5585<br />Smoker: 0","Age: 35<br />LungCapacitycc: 5683<br />Smoker: 0","Age: 38<br />LungCapacitycc: 5734<br />Smoker: 0","Age: 43<br />LungCapacitycc: 5187<br />Smoker: 0","Age: 71<br />LungCapacitycc: 5518<br />Smoker: 0","Age: 66<br />LungCapacitycc: 5959<br />Smoker: 0","Age: 35<br />LungCapacitycc: 5400<br />Smoker: 0","Age: 47<br />LungCapacitycc: 5673<br />Smoker: 0"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":"rgba(248,118,109,1)","opacity":1,"size":5.66929133858268,"symbol":"circle","line":{"width":1.88976377952756,"color":"rgba(248,118,109,1)"}},"hoveron":"points","name":"0","legendgroup":"0","showlegend":true,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[40,35,40,19,33,52,39,58,43,47,58,29,54,37,53,50,49,46,28,47,59,54,42,37,55,40,55,59,38,64,79,23,54,41,50,51],"y":[5133,5415,5463,5308,4234,4783,4858,4686,4940,4553,5484,4625,5438,5399,4906,5042,5254,4641,4735,4874,5203,4823,4690,5397,4651,5205,4980,5180,4636,4945,4900,4713,4620,4644,4925,4959],"text":["Age: 40<br />LungCapacitycc: 5133<br />Smoker: 1","Age: 35<br />LungCapacitycc: 5415<br />Smoker: 1","Age: 40<br />LungCapacitycc: 5463<br />Smoker: 1","Age: 19<br />LungCapacitycc: 5308<br />Smoker: 1","Age: 33<br />LungCapacitycc: 4234<br />Smoker: 1","Age: 52<br />LungCapacitycc: 4783<br />Smoker: 1","Age: 39<br />LungCapacitycc: 4858<br />Smoker: 1","Age: 58<br />LungCapacitycc: 4686<br />Smoker: 1","Age: 43<br />LungCapacitycc: 4940<br />Smoker: 1","Age: 47<br />LungCapacitycc: 4553<br />Smoker: 1","Age: 58<br />LungCapacitycc: 5484<br />Smoker: 1","Age: 29<br />LungCapacitycc: 4625<br />Smoker: 1","Age: 54<br />LungCapacitycc: 5438<br />Smoker: 1","Age: 37<br />LungCapacitycc: 5399<br />Smoker: 1","Age: 53<br />LungCapacitycc: 4906<br />Smoker: 1","Age: 50<br />LungCapacitycc: 5042<br />Smoker: 1","Age: 49<br />LungCapacitycc: 5254<br />Smoker: 1","Age: 46<br />LungCapacitycc: 4641<br />Smoker: 1","Age: 28<br />LungCapacitycc: 4735<br />Smoker: 1","Age: 47<br />LungCapacitycc: 4874<br />Smoker: 1","Age: 59<br />LungCapacitycc: 5203<br />Smoker: 1","Age: 54<br />LungCapacitycc: 4823<br />Smoker: 1","Age: 42<br />LungCapacitycc: 4690<br />Smoker: 1","Age: 37<br />LungCapacitycc: 5397<br />Smoker: 1","Age: 55<br />LungCapacitycc: 4651<br />Smoker: 1","Age: 40<br />LungCapacitycc: 5205<br />Smoker: 1","Age: 55<br />LungCapacitycc: 4980<br />Smoker: 1","Age: 59<br />LungCapacitycc: 5180<br />Smoker: 1","Age: 38<br />LungCapacitycc: 4636<br />Smoker: 1","Age: 64<br />LungCapacitycc: 4945<br />Smoker: 1","Age: 79<br />LungCapacitycc: 4900<br />Smoker: 1","Age: 23<br />LungCapacitycc: 4713<br />Smoker: 1","Age: 54<br />LungCapacitycc: 4620<br />Smoker: 1","Age: 41<br />LungCapacitycc: 4644<br />Smoker: 1","Age: 50<br />LungCapacitycc: 4925<br />Smoker: 1","Age: 51<br />LungCapacitycc: 4959<br />Smoker: 1"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":"rgba(0,191,196,1)","opacity":1,"size":5.66929133858268,"symbol":"circle","line":{"width":1.88976377952756,"color":"rgba(0,191,196,1)"}},"hoveron":"points","name":"1","legendgroup":"1","showlegend":true,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[26,26.7088607594937,27.4177215189873,28.126582278481,28.8354430379747,29.5443037974684,30.253164556962,30.9620253164557,31.6708860759494,32.379746835443,33.0886075949367,33.7974683544304,34.5063291139241,35.2151898734177,35.9240506329114,36.6329113924051,37.3417721518987,38.0506329113924,38.7594936708861,39.4683544303797,40.1772151898734,40.8860759493671,41.5949367088608,42.3037974683544,43.0126582278481,43.7215189873418,44.4303797468354,45.1392405063291,45.8481012658228,46.5569620253165,47.2658227848101,47.9746835443038,48.6835443037975,49.3924050632911,50.1012658227848,50.8101265822785,51.5189873417722,52.2278481012658,52.9367088607595,53.6455696202532,54.3544303797468,55.0632911392405,55.7721518987342,56.4810126582278,57.1898734177215,57.8987341772152,58.6075949367089,59.3164556962025,60.0253164556962,60.7341772151899,61.4430379746835,62.1518987341772,62.8607594936709,63.5696202531646,64.2784810126582,64.9873417721519,65.6962025316456,66.4050632911392,67.1139240506329,67.8227848101266,68.5316455696203,69.2405063291139,69.9493670886076,70.6582278481013,71.3670886075949,72.0759493670886,72.7848101265823,73.4936708860759,74.2025316455696,74.9113924050633,75.620253164557,76.3291139240506,77.0379746835443,77.746835443038,78.4556962025316,79.1645569620253,79.873417721519,80.5822784810127,81.2911392405063,82],"y":[5497.7511672964,5499.47285391625,5501.19454053611,5502.91622715596,5504.63791377581,5506.35960039567,5508.08128701552,5509.80297363537,5511.52466025523,5513.24634687508,5514.96803349493,5516.68972011478,5518.41140673464,5520.13309335449,5521.85477997434,5523.5764665942,5525.29815321405,5527.0198398339,5528.74152645375,5530.46321307361,5532.18489969346,5533.90658631331,5535.62827293317,5537.34995955302,5539.07164617287,5540.79333279273,5542.51501941258,5544.23670603243,5545.95839265228,5547.68007927214,5549.40176589199,5551.12345251184,5552.8451391317,5554.56682575155,5556.2885123714,5558.01019899126,5559.73188561111,5561.45357223096,5563.17525885081,5564.89694547067,5566.61863209052,5568.34031871037,5570.06200533023,5571.78369195008,5573.50537856993,5575.22706518979,5576.94875180964,5578.67043842949,5580.39212504934,5582.1138116692,5583.83549828905,5585.5571849089,5587.27887152876,5589.00055814861,5590.72224476846,5592.44393138831,5594.16561800817,5595.88730462802,5597.60899124787,5599.33067786773,5601.05236448758,5602.77405110743,5604.49573772729,5606.21742434714,5607.93911096699,5609.66079758684,5611.3824842067,5613.10417082655,5614.8258574464,5616.54754406626,5618.26923068611,5619.99091730596,5621.71260392581,5623.43429054567,5625.15597716552,5626.87766378537,5628.59935040523,5630.32103702508,5632.04272364493,5633.76441026479],"text":["Age: 26.00000<br />LungCapacitycc: 5497.751<br />Smoker: 0","Age: 26.70886<br />LungCapacitycc: 5499.473<br />Smoker: 0","Age: 27.41772<br />LungCapacitycc: 5501.195<br />Smoker: 0","Age: 28.12658<br />LungCapacitycc: 5502.916<br />Smoker: 0","Age: 28.83544<br />LungCapacitycc: 5504.638<br />Smoker: 0","Age: 29.54430<br />LungCapacitycc: 5506.360<br />Smoker: 0","Age: 30.25316<br />LungCapacitycc: 5508.081<br />Smoker: 0","Age: 30.96203<br />LungCapacitycc: 5509.803<br />Smoker: 0","Age: 31.67089<br />LungCapacitycc: 5511.525<br />Smoker: 0","Age: 32.37975<br />LungCapacitycc: 5513.246<br />Smoker: 0","Age: 33.08861<br />LungCapacitycc: 5514.968<br />Smoker: 0","Age: 33.79747<br />LungCapacitycc: 5516.690<br />Smoker: 0","Age: 34.50633<br />LungCapacitycc: 5518.411<br />Smoker: 0","Age: 35.21519<br />LungCapacitycc: 5520.133<br />Smoker: 0","Age: 35.92405<br />LungCapacitycc: 5521.855<br />Smoker: 0","Age: 36.63291<br />LungCapacitycc: 5523.576<br />Smoker: 0","Age: 37.34177<br />LungCapacitycc: 5525.298<br />Smoker: 0","Age: 38.05063<br />LungCapacitycc: 5527.020<br />Smoker: 0","Age: 38.75949<br />LungCapacitycc: 5528.742<br />Smoker: 0","Age: 39.46835<br />LungCapacitycc: 5530.463<br />Smoker: 0","Age: 40.17722<br />LungCapacitycc: 5532.185<br />Smoker: 0","Age: 40.88608<br />LungCapacitycc: 5533.907<br />Smoker: 0","Age: 41.59494<br />LungCapacitycc: 5535.628<br />Smoker: 0","Age: 42.30380<br />LungCapacitycc: 5537.350<br />Smoker: 0","Age: 43.01266<br />LungCapacitycc: 5539.072<br />Smoker: 0","Age: 43.72152<br />LungCapacitycc: 5540.793<br />Smoker: 0","Age: 44.43038<br />LungCapacitycc: 5542.515<br />Smoker: 0","Age: 45.13924<br />LungCapacitycc: 5544.237<br />Smoker: 0","Age: 45.84810<br />LungCapacitycc: 5545.958<br />Smoker: 0","Age: 46.55696<br />LungCapacitycc: 5547.680<br />Smoker: 0","Age: 47.26582<br />LungCapacitycc: 5549.402<br />Smoker: 0","Age: 47.97468<br />LungCapacitycc: 5551.123<br />Smoker: 0","Age: 48.68354<br />LungCapacitycc: 5552.845<br />Smoker: 0","Age: 49.39241<br />LungCapacitycc: 5554.567<br />Smoker: 0","Age: 50.10127<br />LungCapacitycc: 5556.289<br />Smoker: 0","Age: 50.81013<br />LungCapacitycc: 5558.010<br />Smoker: 0","Age: 51.51899<br />LungCapacitycc: 5559.732<br />Smoker: 0","Age: 52.22785<br />LungCapacitycc: 5561.454<br />Smoker: 0","Age: 52.93671<br />LungCapacitycc: 5563.175<br />Smoker: 0","Age: 53.64557<br />LungCapacitycc: 5564.897<br />Smoker: 0","Age: 54.35443<br />LungCapacitycc: 5566.619<br />Smoker: 0","Age: 55.06329<br />LungCapacitycc: 5568.340<br />Smoker: 0","Age: 55.77215<br />LungCapacitycc: 5570.062<br />Smoker: 0","Age: 56.48101<br />LungCapacitycc: 5571.784<br />Smoker: 0","Age: 57.18987<br />LungCapacitycc: 5573.505<br />Smoker: 0","Age: 57.89873<br />LungCapacitycc: 5575.227<br />Smoker: 0","Age: 58.60759<br />LungCapacitycc: 5576.949<br />Smoker: 0","Age: 59.31646<br />LungCapacitycc: 5578.670<br />Smoker: 0","Age: 60.02532<br />LungCapacitycc: 5580.392<br />Smoker: 0","Age: 60.73418<br />LungCapacitycc: 5582.114<br />Smoker: 0","Age: 61.44304<br />LungCapacitycc: 5583.835<br />Smoker: 0","Age: 62.15190<br />LungCapacitycc: 5585.557<br />Smoker: 0","Age: 62.86076<br />LungCapacitycc: 5587.279<br />Smoker: 0","Age: 63.56962<br />LungCapacitycc: 5589.001<br />Smoker: 0","Age: 64.27848<br />LungCapacitycc: 5590.722<br />Smoker: 0","Age: 64.98734<br />LungCapacitycc: 5592.444<br />Smoker: 0","Age: 65.69620<br />LungCapacitycc: 5594.166<br />Smoker: 0","Age: 66.40506<br />LungCapacitycc: 5595.887<br />Smoker: 0","Age: 67.11392<br />LungCapacitycc: 5597.609<br />Smoker: 0","Age: 67.82278<br />LungCapacitycc: 5599.331<br />Smoker: 0","Age: 68.53165<br />LungCapacitycc: 5601.052<br />Smoker: 0","Age: 69.24051<br />LungCapacitycc: 5602.774<br />Smoker: 0","Age: 69.94937<br />LungCapacitycc: 5604.496<br />Smoker: 0","Age: 70.65823<br />LungCapacitycc: 5606.217<br />Smoker: 0","Age: 71.36709<br />LungCapacitycc: 5607.939<br />Smoker: 0","Age: 72.07595<br />LungCapacitycc: 5609.661<br />Smoker: 0","Age: 72.78481<br />LungCapacitycc: 5611.382<br />Smoker: 0","Age: 73.49367<br />LungCapacitycc: 5613.104<br />Smoker: 0","Age: 74.20253<br />LungCapacitycc: 5614.826<br />Smoker: 0","Age: 74.91139<br />LungCapacitycc: 5616.548<br />Smoker: 0","Age: 75.62025<br />LungCapacitycc: 5618.269<br />Smoker: 0","Age: 76.32911<br />LungCapacitycc: 5619.991<br />Smoker: 0","Age: 77.03797<br />LungCapacitycc: 5621.713<br />Smoker: 0","Age: 77.74684<br />LungCapacitycc: 5623.434<br />Smoker: 0","Age: 78.45570<br />LungCapacitycc: 5625.156<br />Smoker: 0","Age: 79.16456<br />LungCapacitycc: 5626.878<br />Smoker: 0","Age: 79.87342<br />LungCapacitycc: 5628.599<br />Smoker: 0","Age: 80.58228<br />LungCapacitycc: 5630.321<br />Smoker: 0","Age: 81.29114<br />LungCapacitycc: 5632.043<br />Smoker: 0","Age: 82.00000<br />LungCapacitycc: 5633.764<br />Smoker: 0"],"type":"scatter","mode":"lines","name":"0","line":{"width":3.77952755905512,"color":"rgba(248,118,109,1)","dash":"solid"},"hoveron":"points","legendgroup":"0","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[19,19.7594936708861,20.5189873417722,21.2784810126582,22.0379746835443,22.7974683544304,23.5569620253165,24.3164556962025,25.0759493670886,25.8354430379747,26.5949367088608,27.3544303797468,28.1139240506329,28.873417721519,29.6329113924051,30.3924050632911,31.1518987341772,31.9113924050633,32.6708860759494,33.4303797468354,34.1898734177215,34.9493670886076,35.7088607594937,36.4683544303797,37.2278481012658,37.9873417721519,38.746835443038,39.5063291139241,40.2658227848101,41.0253164556962,41.7848101265823,42.5443037974684,43.3037974683544,44.0632911392405,44.8227848101266,45.5822784810127,46.3417721518987,47.1012658227848,47.8607594936709,48.620253164557,49.379746835443,50.1392405063291,50.8987341772152,51.6582278481013,52.4177215189873,53.1772151898734,53.9367088607595,54.6962025316456,55.4556962025316,56.2151898734177,56.9746835443038,57.7341772151899,58.493670886076,59.253164556962,60.0126582278481,60.7721518987342,61.5316455696203,62.2911392405063,63.0506329113924,63.8101265822785,64.5696202531646,65.3291139240506,66.0886075949367,66.8481012658228,67.6075949367089,68.3670886075949,69.126582278481,69.8860759493671,70.6455696202532,71.4050632911392,72.1645569620253,72.9240506329114,73.6835443037975,74.4430379746835,75.2025316455696,75.9620253164557,76.7215189873418,77.4810126582279,78.2405063291139,79],"y":[4917.45352255777,4918.3999056222,4919.34628868662,4920.29267175105,4921.23905481547,4922.1854378799,4923.13182094432,4924.07820400875,4925.02458707317,4925.97097013759,4926.91735320202,4927.86373626644,4928.81011933087,4929.75650239529,4930.70288545972,4931.64926852414,4932.59565158857,4933.54203465299,4934.48841771742,4935.43480078184,4936.38118384626,4937.32756691069,4938.27394997511,4939.22033303954,4940.16671610396,4941.11309916839,4942.05948223281,4943.00586529724,4943.95224836166,4944.89863142609,4945.84501449051,4946.79139755493,4947.73778061936,4948.68416368378,4949.63054674821,4950.57692981263,4951.52331287706,4952.46969594148,4953.41607900591,4954.36246207033,4955.30884513475,4956.25522819918,4957.2016112636,4958.14799432803,4959.09437739245,4960.04076045688,4960.9871435213,4961.93352658573,4962.87990965015,4963.82629271458,4964.772675779,4965.71905884343,4966.66544190785,4967.61182497227,4968.5582080367,4969.50459110112,4970.45097416555,4971.39735722997,4972.3437402944,4973.29012335882,4974.23650642325,4975.18288948767,4976.1292725521,4977.07565561652,4978.02203868094,4978.96842174537,4979.91480480979,4980.86118787422,4981.80757093864,4982.75395400307,4983.70033706749,4984.64672013192,4985.59310319634,4986.53948626077,4987.48586932519,4988.43225238961,4989.37863545404,4990.32501851846,4991.27140158289,4992.21778464731],"text":["Age: 19.00000<br />LungCapacitycc: 4917.454<br />Smoker: 1","Age: 19.75949<br />LungCapacitycc: 4918.400<br />Smoker: 1","Age: 20.51899<br />LungCapacitycc: 4919.346<br />Smoker: 1","Age: 21.27848<br />LungCapacitycc: 4920.293<br />Smoker: 1","Age: 22.03797<br />LungCapacitycc: 4921.239<br />Smoker: 1","Age: 22.79747<br />LungCapacitycc: 4922.185<br />Smoker: 1","Age: 23.55696<br />LungCapacitycc: 4923.132<br />Smoker: 1","Age: 24.31646<br />LungCapacitycc: 4924.078<br />Smoker: 1","Age: 25.07595<br />LungCapacitycc: 4925.025<br />Smoker: 1","Age: 25.83544<br />LungCapacitycc: 4925.971<br />Smoker: 1","Age: 26.59494<br />LungCapacitycc: 4926.917<br />Smoker: 1","Age: 27.35443<br />LungCapacitycc: 4927.864<br />Smoker: 1","Age: 28.11392<br />LungCapacitycc: 4928.810<br />Smoker: 1","Age: 28.87342<br />LungCapacitycc: 4929.757<br />Smoker: 1","Age: 29.63291<br />LungCapacitycc: 4930.703<br />Smoker: 1","Age: 30.39241<br />LungCapacitycc: 4931.649<br />Smoker: 1","Age: 31.15190<br />LungCapacitycc: 4932.596<br />Smoker: 1","Age: 31.91139<br />LungCapacitycc: 4933.542<br />Smoker: 1","Age: 32.67089<br />LungCapacitycc: 4934.488<br />Smoker: 1","Age: 33.43038<br />LungCapacitycc: 4935.435<br />Smoker: 1","Age: 34.18987<br />LungCapacitycc: 4936.381<br />Smoker: 1","Age: 34.94937<br />LungCapacitycc: 4937.328<br />Smoker: 1","Age: 35.70886<br />LungCapacitycc: 4938.274<br />Smoker: 1","Age: 36.46835<br />LungCapacitycc: 4939.220<br />Smoker: 1","Age: 37.22785<br />LungCapacitycc: 4940.167<br />Smoker: 1","Age: 37.98734<br />LungCapacitycc: 4941.113<br />Smoker: 1","Age: 38.74684<br />LungCapacitycc: 4942.059<br />Smoker: 1","Age: 39.50633<br />LungCapacitycc: 4943.006<br />Smoker: 1","Age: 40.26582<br />LungCapacitycc: 4943.952<br />Smoker: 1","Age: 41.02532<br />LungCapacitycc: 4944.899<br />Smoker: 1","Age: 41.78481<br />LungCapacitycc: 4945.845<br />Smoker: 1","Age: 42.54430<br />LungCapacitycc: 4946.791<br />Smoker: 1","Age: 43.30380<br />LungCapacitycc: 4947.738<br />Smoker: 1","Age: 44.06329<br />LungCapacitycc: 4948.684<br />Smoker: 1","Age: 44.82278<br />LungCapacitycc: 4949.631<br />Smoker: 1","Age: 45.58228<br />LungCapacitycc: 4950.577<br />Smoker: 1","Age: 46.34177<br />LungCapacitycc: 4951.523<br />Smoker: 1","Age: 47.10127<br />LungCapacitycc: 4952.470<br />Smoker: 1","Age: 47.86076<br />LungCapacitycc: 4953.416<br />Smoker: 1","Age: 48.62025<br />LungCapacitycc: 4954.362<br />Smoker: 1","Age: 49.37975<br />LungCapacitycc: 4955.309<br />Smoker: 1","Age: 50.13924<br />LungCapacitycc: 4956.255<br />Smoker: 1","Age: 50.89873<br />LungCapacitycc: 4957.202<br />Smoker: 1","Age: 51.65823<br />LungCapacitycc: 4958.148<br />Smoker: 1","Age: 52.41772<br />LungCapacitycc: 4959.094<br />Smoker: 1","Age: 53.17722<br />LungCapacitycc: 4960.041<br />Smoker: 1","Age: 53.93671<br />LungCapacitycc: 4960.987<br />Smoker: 1","Age: 54.69620<br />LungCapacitycc: 4961.934<br />Smoker: 1","Age: 55.45570<br />LungCapacitycc: 4962.880<br />Smoker: 1","Age: 56.21519<br />LungCapacitycc: 4963.826<br />Smoker: 1","Age: 56.97468<br />LungCapacitycc: 4964.773<br />Smoker: 1","Age: 57.73418<br />LungCapacitycc: 4965.719<br />Smoker: 1","Age: 58.49367<br />LungCapacitycc: 4966.665<br />Smoker: 1","Age: 59.25316<br />LungCapacitycc: 4967.612<br />Smoker: 1","Age: 60.01266<br />LungCapacitycc: 4968.558<br />Smoker: 1","Age: 60.77215<br />LungCapacitycc: 4969.505<br />Smoker: 1","Age: 61.53165<br />LungCapacitycc: 4970.451<br />Smoker: 1","Age: 62.29114<br />LungCapacitycc: 4971.397<br />Smoker: 1","Age: 63.05063<br />LungCapacitycc: 4972.344<br />Smoker: 1","Age: 63.81013<br />LungCapacitycc: 4973.290<br />Smoker: 1","Age: 64.56962<br />LungCapacitycc: 4974.237<br />Smoker: 1","Age: 65.32911<br />LungCapacitycc: 4975.183<br />Smoker: 1","Age: 66.08861<br />LungCapacitycc: 4976.129<br />Smoker: 1","Age: 66.84810<br />LungCapacitycc: 4977.076<br />Smoker: 1","Age: 67.60759<br />LungCapacitycc: 4978.022<br />Smoker: 1","Age: 68.36709<br />LungCapacitycc: 4978.968<br />Smoker: 1","Age: 69.12658<br />LungCapacitycc: 4979.915<br />Smoker: 1","Age: 69.88608<br />LungCapacitycc: 4980.861<br />Smoker: 1","Age: 70.64557<br />LungCapacitycc: 4981.808<br />Smoker: 1","Age: 71.40506<br />LungCapacitycc: 4982.754<br />Smoker: 1","Age: 72.16456<br />LungCapacitycc: 4983.700<br />Smoker: 1","Age: 72.92405<br />LungCapacitycc: 4984.647<br />Smoker: 1","Age: 73.68354<br />LungCapacitycc: 4985.593<br />Smoker: 1","Age: 74.44304<br />LungCapacitycc: 4986.539<br />Smoker: 1","Age: 75.20253<br />LungCapacitycc: 4987.486<br />Smoker: 1","Age: 75.96203<br />LungCapacitycc: 4988.432<br />Smoker: 1","Age: 76.72152<br />LungCapacitycc: 4989.379<br />Smoker: 1","Age: 77.48101<br />LungCapacitycc: 4990.325<br />Smoker: 1","Age: 78.24051<br />LungCapacitycc: 4991.271<br />Smoker: 1","Age: 79.00000<br />LungCapacitycc: 4992.218<br />Smoker: 1"],"type":"scatter","mode":"lines","name":"1","line":{"width":3.77952755905512,"color":"rgba(0,191,196,1)","dash":"solid"},"hoveron":"points","legendgroup":"1","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null}],"layout":{"margin":{"t":28.1765601217656,"r":7.30593607305936,"b":42.130898021309,"l":48.9497716894977},"font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187},"xaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[15.85,85.15],"tickmode":"array","ticktext":["20","40","60","80"],"tickvals":[20,40,60,80],"categoryorder":"array","categoryarray":["20","40","60","80"],"nticks":null,"ticks":"","tickcolor":null,"ticklen":3.65296803652968,"tickwidth":0,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.689497716895},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176,"zeroline":false,"anchor":"y","title":{"text":"Age","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"yaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[4132.65,6362.35],"tickmode":"array","ticktext":["4500","5000","5500","6000"],"tickvals":[4500,5000,5500,6000],"categoryorder":"array","categoryarray":["4500","5000","5500","6000"],"nticks":null,"ticks":"","tickcolor":null,"ticklen":3.65296803652968,"tickwidth":0,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.689497716895},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176,"zeroline":false,"anchor":"x","title":{"text":"LungCapacitycc","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"shapes":[{"type":"rect","fillcolor":null,"line":{"color":null,"width":0,"linetype":[]},"yref":"paper","xref":"paper","x0":0,"x1":1,"y0":0,"y1":1}],"showlegend":true,"legend":{"bgcolor":null,"bordercolor":null,"borderwidth":0,"font":{"color":"rgba(0,0,0,1)","family":"","size":11.689497716895},"y":0.927821522309711},"annotations":[{"text":"Smoker","x":1.02,"y":1,"showarrow":false,"ax":0,"ay":0,"font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187},"xref":"paper","yref":"paper","textangle":-0,"xanchor":"left","yanchor":"bottom","legendTitle":true}],"hovermode":"closest","barmode":"relative"},"config":{"doubleClick":"reset","showSendToCloud":false},"source":"A","attrs":{"1ecf1b1db69b":{"x":{},"y":{},"colour":{},"type":"scatter"},"1ecf3bbf8805":{"x":{},"y":{},"colour":{}}},"cur_data":"1ecf1b1db69b","visdat":{"1ecf1b1db69b":["function (y) ","x"],"1ecf3bbf8805":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.2,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- ## Interaction **Interaction model equation: ** With two independent variables: `$$Y_i = \beta_0 + \beta_1 \cdot X_{i1} + \beta_2 \cdot X_{i2} + \beta_3 \cdot X_{i1} X_{i2} + \varepsilon_i, \ \ \ i = 1, ..., n$$` With three independent variables: `$$Y_i = \beta_0 + \beta_1 \cdot X_{i1} + \beta_2 \cdot X_{i2} + \beta_3 \cdot X_{i3} + \\ \beta_4 \cdot X_{i1} X_{i2} + \beta_5 \cdot X_{i2} X_{i3} + \beta_6 \cdot X_{i1} X_{i3} + \varepsilon_i, \ \ \ i = 1, ..., n$$` This reveals an interactive relation: - slopes are related - regression lines are non-parallel --- ## Demo 2: Interaction [Stress Data](https://rdrr.io/cran/datarium/man/stress.html) ```r *dat2 <- datarium::stress dplyr::glimpse(dat2) ``` ``` ## Observations: 60 ## Variables: 5 ## $ id <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, … ## $ score <dbl> 95.6, 82.2, 97.2, 96.4, 81.4, 83.6, 89.4, 83.8, 83.3, 85.7,… ## $ treatment <fct> yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes,… ## $ exercise <fct> low, low, low, low, low, low, low, low, low, low, moderate,… ## $ age <dbl> 59, 65, 70, 66, 61, 65, 57, 61, 58, 55, 62, 61, 60, 59, 55,… ``` ```r summary(mod1 <- lm(score ~ treatment + exercise + age, data = dat2))$coefficients ``` ``` ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 55.72934446 10.9188850 5.10394099 4.272045e-06 ## treatmentno 4.32528628 1.3774437 3.14008203 2.716774e-03 ## exercisemoderate 0.08735408 1.6903218 0.05167896 9.589717e-01 ## exercisehigh -9.61841026 1.8474096 -5.20643089 2.955621e-06 ## age 0.49811005 0.1764842 2.82240615 6.621719e-03 ``` --- ## Demo 2: Interaction (Continued) <div id="htmlwidget-6ebb3e2640ccb5978111" style="width:720px;height:432px;" class="plotly html-widget"></div> <script type="application/json" data-for="htmlwidget-6ebb3e2640ccb5978111">{"x":{"data":[{"x":[59,65,70,66,61,65,57,61,58,55,62,61,60,59,55,57,60,63,62,57,58,56,57,59,59,60,55,53,55,58],"y":[95.6,82.2,97.2,96.4,81.4,83.6,89.4,83.8,83.3,85.7,97.2,78.2,78.9,91.8,86.9,84.1,88.6,89.8,87.3,85.4,81.8,65.8,68.1,70,69.9,75.1,72.3,70.9,71.5,72.5],"text":["age: 59<br />score: 95.6<br />treatment: yes","age: 65<br />score: 82.2<br />treatment: yes","age: 70<br />score: 97.2<br />treatment: yes","age: 66<br />score: 96.4<br />treatment: yes","age: 61<br />score: 81.4<br />treatment: yes","age: 65<br />score: 83.6<br />treatment: yes","age: 57<br />score: 89.4<br />treatment: yes","age: 61<br />score: 83.8<br />treatment: yes","age: 58<br />score: 83.3<br />treatment: yes","age: 55<br />score: 85.7<br />treatment: yes","age: 62<br />score: 97.2<br />treatment: yes","age: 61<br />score: 78.2<br />treatment: yes","age: 60<br />score: 78.9<br />treatment: yes","age: 59<br />score: 91.8<br />treatment: yes","age: 55<br />score: 86.9<br />treatment: yes","age: 57<br />score: 84.1<br />treatment: yes","age: 60<br />score: 88.6<br />treatment: yes","age: 63<br />score: 89.8<br />treatment: yes","age: 62<br />score: 87.3<br />treatment: yes","age: 57<br />score: 85.4<br />treatment: yes","age: 58<br />score: 81.8<br />treatment: yes","age: 56<br />score: 65.8<br />treatment: yes","age: 57<br />score: 68.1<br />treatment: yes","age: 59<br />score: 70.0<br />treatment: yes","age: 59<br />score: 69.9<br />treatment: yes","age: 60<br />score: 75.1<br />treatment: yes","age: 55<br />score: 72.3<br />treatment: yes","age: 53<br />score: 70.9<br />treatment: yes","age: 55<br />score: 71.5<br />treatment: yes","age: 58<br />score: 72.5<br />treatment: yes"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":"rgba(248,118,109,1)","opacity":1,"size":5.66929133858268,"symbol":"circle","line":{"width":1.88976377952756,"color":"rgba(248,118,109,1)"}},"hoveron":"points","name":"yes","legendgroup":"yes","showlegend":true,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[68,62,61,54,59,63,60,67,60,67,75,54,57,62,65,60,58,61,65,57,56,58,58,58,52,53,60,62,61,61],"y":[84.9,96.1,94.6,82.5,90.7,87,86.8,93.3,87.6,92.4,100,80.5,92.9,84,88.4,91.1,85.7,91.3,92.3,87.9,91.7,88.6,75.8,75.7,75.3,82.4,80.1,86,81.8,82.5],"text":["age: 68<br />score: 84.9<br />treatment: no","age: 62<br />score: 96.1<br />treatment: no","age: 61<br />score: 94.6<br />treatment: no","age: 54<br />score: 82.5<br />treatment: no","age: 59<br />score: 90.7<br />treatment: no","age: 63<br />score: 87.0<br />treatment: no","age: 60<br />score: 86.8<br />treatment: no","age: 67<br />score: 93.3<br />treatment: no","age: 60<br />score: 87.6<br />treatment: no","age: 67<br />score: 92.4<br />treatment: no","age: 75<br />score: 100.0<br />treatment: no","age: 54<br />score: 80.5<br />treatment: no","age: 57<br />score: 92.9<br />treatment: no","age: 62<br />score: 84.0<br />treatment: no","age: 65<br />score: 88.4<br />treatment: no","age: 60<br />score: 91.1<br />treatment: no","age: 58<br />score: 85.7<br />treatment: no","age: 61<br />score: 91.3<br />treatment: no","age: 65<br />score: 92.3<br />treatment: no","age: 57<br />score: 87.9<br />treatment: no","age: 56<br />score: 91.7<br />treatment: no","age: 58<br />score: 88.6<br />treatment: no","age: 58<br />score: 75.8<br />treatment: no","age: 58<br />score: 75.7<br />treatment: no","age: 52<br />score: 75.3<br />treatment: no","age: 53<br />score: 82.4<br />treatment: no","age: 60<br />score: 80.1<br />treatment: no","age: 62<br />score: 86.0<br />treatment: no","age: 61<br />score: 81.8<br />treatment: no","age: 61<br />score: 82.5<br />treatment: no"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":"rgba(0,191,196,1)","opacity":1,"size":5.66929133858268,"symbol":"circle","line":{"width":1.88976377952756,"color":"rgba(0,191,196,1)"}},"hoveron":"points","name":"no","legendgroup":"no","showlegend":true,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[53,53.2151898734177,53.4303797468354,53.6455696202532,53.8607594936709,54.0759493670886,54.2911392405063,54.5063291139241,54.7215189873418,54.9367088607595,55.1518987341772,55.3670886075949,55.5822784810127,55.7974683544304,56.0126582278481,56.2278481012658,56.4430379746835,56.6582278481013,56.873417721519,57.0886075949367,57.3037974683544,57.5189873417722,57.7341772151899,57.9493670886076,58.1645569620253,58.379746835443,58.5949367088608,58.8101265822785,59.0253164556962,59.2405063291139,59.4556962025316,59.6708860759494,59.8860759493671,60.1012658227848,60.3164556962025,60.5316455696203,60.746835443038,60.9620253164557,61.1772151898734,61.3924050632911,61.6075949367089,61.8227848101266,62.0379746835443,62.253164556962,62.4683544303797,62.6835443037975,62.8987341772152,63.1139240506329,63.3291139240506,63.5443037974684,63.7594936708861,63.9746835443038,64.1898734177215,64.4050632911392,64.620253164557,64.8354430379747,65.0506329113924,65.2658227848101,65.4810126582279,65.6962025316456,65.9113924050633,66.126582278481,66.3417721518987,66.5569620253165,66.7721518987342,66.9873417721519,67.2025316455696,67.4177215189873,67.6329113924051,67.8481012658228,68.0632911392405,68.2784810126582,68.4936708860759,68.7088607594937,68.9240506329114,69.1392405063291,69.3544303797468,69.5696202531646,69.7848101265823,70],"y":[73.8635755181034,74.1409728084404,74.4183700987773,74.6957673891142,74.9731646794512,75.2505619697881,75.527959260125,75.805356550462,76.0827538407989,76.3601511311359,76.6375484214728,76.9149457118097,77.1923430021466,77.4697402924836,77.7471375828205,78.0245348731574,78.3019321634944,78.5793294538313,78.8567267441683,79.1341240345052,79.4115213248421,79.6889186151791,79.966315905516,80.2437131958529,80.5211104861899,80.7985077765268,81.0759050668638,81.3533023572007,81.6306996475376,81.9080969378746,82.1854942282115,82.4628915185484,82.7402888088854,83.0176860992223,83.2950833895592,83.5724806798962,83.8498779702331,84.12727526057,84.404672550907,84.6820698412439,84.9594671315809,85.2368644219178,85.5142617122547,85.7916590025917,86.0690562929286,86.3464535832655,86.6238508736025,86.9012481639394,87.1786454542763,87.4560427446133,87.7334400349502,88.0108373252872,88.2882346156241,88.565631905961,88.8430291962979,89.1204264866349,89.3978237769718,89.6752210673088,89.9526183576457,90.2300156479826,90.5074129383196,90.7848102286565,91.0622075189934,91.3396048093304,91.6170020996673,91.8943993900042,92.1717966803412,92.4491939706781,92.7265912610151,93.003988551352,93.2813858416889,93.5587831320259,93.8361804223628,94.1135777126997,94.3909750030367,94.6683722933736,94.9457695837106,95.2231668740475,95.5005641643844,95.7779614547213],"text":["age: 53.00000<br />score: 73.86358<br />treatment: yes","age: 53.21519<br />score: 74.14097<br />treatment: yes","age: 53.43038<br />score: 74.41837<br />treatment: yes","age: 53.64557<br />score: 74.69577<br />treatment: yes","age: 53.86076<br />score: 74.97316<br />treatment: yes","age: 54.07595<br />score: 75.25056<br />treatment: yes","age: 54.29114<br />score: 75.52796<br />treatment: yes","age: 54.50633<br />score: 75.80536<br />treatment: yes","age: 54.72152<br />score: 76.08275<br />treatment: yes","age: 54.93671<br />score: 76.36015<br />treatment: yes","age: 55.15190<br />score: 76.63755<br />treatment: yes","age: 55.36709<br />score: 76.91495<br />treatment: yes","age: 55.58228<br />score: 77.19234<br />treatment: yes","age: 55.79747<br />score: 77.46974<br />treatment: yes","age: 56.01266<br />score: 77.74714<br />treatment: yes","age: 56.22785<br />score: 78.02453<br />treatment: yes","age: 56.44304<br />score: 78.30193<br />treatment: yes","age: 56.65823<br />score: 78.57933<br />treatment: yes","age: 56.87342<br />score: 78.85673<br />treatment: yes","age: 57.08861<br />score: 79.13412<br />treatment: yes","age: 57.30380<br />score: 79.41152<br />treatment: yes","age: 57.51899<br />score: 79.68892<br />treatment: yes","age: 57.73418<br />score: 79.96632<br />treatment: yes","age: 57.94937<br />score: 80.24371<br />treatment: yes","age: 58.16456<br />score: 80.52111<br />treatment: yes","age: 58.37975<br />score: 80.79851<br />treatment: yes","age: 58.59494<br />score: 81.07591<br />treatment: yes","age: 58.81013<br />score: 81.35330<br />treatment: yes","age: 59.02532<br />score: 81.63070<br />treatment: yes","age: 59.24051<br />score: 81.90810<br />treatment: yes","age: 59.45570<br />score: 82.18549<br />treatment: yes","age: 59.67089<br />score: 82.46289<br />treatment: yes","age: 59.88608<br />score: 82.74029<br />treatment: yes","age: 60.10127<br />score: 83.01769<br />treatment: yes","age: 60.31646<br />score: 83.29508<br />treatment: yes","age: 60.53165<br />score: 83.57248<br />treatment: yes","age: 60.74684<br />score: 83.84988<br />treatment: yes","age: 60.96203<br />score: 84.12728<br />treatment: yes","age: 61.17722<br />score: 84.40467<br />treatment: yes","age: 61.39241<br />score: 84.68207<br />treatment: yes","age: 61.60759<br />score: 84.95947<br />treatment: yes","age: 61.82278<br />score: 85.23686<br />treatment: yes","age: 62.03797<br />score: 85.51426<br />treatment: yes","age: 62.25316<br />score: 85.79166<br />treatment: yes","age: 62.46835<br />score: 86.06906<br />treatment: yes","age: 62.68354<br />score: 86.34645<br />treatment: yes","age: 62.89873<br />score: 86.62385<br />treatment: yes","age: 63.11392<br />score: 86.90125<br />treatment: yes","age: 63.32911<br />score: 87.17865<br />treatment: yes","age: 63.54430<br />score: 87.45604<br />treatment: yes","age: 63.75949<br />score: 87.73344<br />treatment: yes","age: 63.97468<br />score: 88.01084<br />treatment: yes","age: 64.18987<br />score: 88.28823<br />treatment: yes","age: 64.40506<br />score: 88.56563<br />treatment: yes","age: 64.62025<br />score: 88.84303<br />treatment: yes","age: 64.83544<br />score: 89.12043<br />treatment: yes","age: 65.05063<br />score: 89.39782<br />treatment: yes","age: 65.26582<br />score: 89.67522<br />treatment: yes","age: 65.48101<br />score: 89.95262<br />treatment: yes","age: 65.69620<br />score: 90.23002<br />treatment: yes","age: 65.91139<br />score: 90.50741<br />treatment: yes","age: 66.12658<br />score: 90.78481<br />treatment: yes","age: 66.34177<br />score: 91.06221<br />treatment: yes","age: 66.55696<br />score: 91.33960<br />treatment: yes","age: 66.77215<br />score: 91.61700<br />treatment: yes","age: 66.98734<br />score: 91.89440<br />treatment: yes","age: 67.20253<br />score: 92.17180<br />treatment: yes","age: 67.41772<br />score: 92.44919<br />treatment: yes","age: 67.63291<br />score: 92.72659<br />treatment: yes","age: 67.84810<br />score: 93.00399<br />treatment: yes","age: 68.06329<br />score: 93.28139<br />treatment: yes","age: 68.27848<br />score: 93.55878<br />treatment: yes","age: 68.49367<br />score: 93.83618<br />treatment: yes","age: 68.70886<br />score: 94.11358<br />treatment: yes","age: 68.92405<br />score: 94.39098<br />treatment: yes","age: 69.13924<br />score: 94.66837<br />treatment: yes","age: 69.35443<br />score: 94.94577<br />treatment: yes","age: 69.56962<br />score: 95.22317<br />treatment: yes","age: 69.78481<br />score: 95.50056<br />treatment: yes","age: 70.00000<br />score: 95.77796<br />treatment: yes"],"type":"scatter","mode":"lines","name":"yes","line":{"width":3.77952755905512,"color":"rgba(248,118,109,1)","dash":"solid"},"hoveron":"points","legendgroup":"yes","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[52,52.2911392405063,52.5822784810127,52.873417721519,53.1645569620253,53.4556962025316,53.746835443038,54.0379746835443,54.3291139240506,54.620253164557,54.9113924050633,55.2025316455696,55.4936708860759,55.7848101265823,56.0759493670886,56.3670886075949,56.6582278481013,56.9493670886076,57.2405063291139,57.5316455696203,57.8227848101266,58.1139240506329,58.4050632911392,58.6962025316456,58.9873417721519,59.2784810126582,59.5696202531646,59.8607594936709,60.1518987341772,60.4430379746835,60.7341772151899,61.0253164556962,61.3164556962025,61.6075949367089,61.8987341772152,62.1898734177215,62.4810126582278,62.7721518987342,63.0632911392405,63.3544303797468,63.6455696202532,63.9367088607595,64.2278481012658,64.5189873417721,64.8101265822785,65.1012658227848,65.3924050632911,65.6835443037975,65.9746835443038,66.2658227848101,66.5569620253165,66.8481012658228,67.1392405063291,67.4303797468354,67.7215189873418,68.0126582278481,68.3037974683544,68.5949367088608,68.8860759493671,69.1772151898734,69.4683544303797,69.7594936708861,70.0506329113924,70.3417721518987,70.6329113924051,70.9240506329114,71.2151898734177,71.5063291139241,71.7974683544304,72.0886075949367,72.379746835443,72.6708860759494,72.9620253164557,73.253164556962,73.5443037974684,73.8354430379747,74.126582278481,74.4177215189873,74.7088607594937,75],"y":[80.8824141920555,81.0926620843849,81.3029099767143,81.5131578690437,81.7234057613731,81.9336536537025,82.1439015460319,82.3541494383613,82.5643973306907,82.7746452230201,82.9848931153495,83.1951410076789,83.4053889000083,83.6156367923377,83.8258846846671,84.0361325769965,84.2463804693259,84.4566283616553,84.6668762539847,84.8771241463141,85.0873720386435,85.2976199309729,85.5078678233023,85.7181157156317,85.9283636079611,86.1386115002905,86.3488593926199,86.5591072849492,86.7693551772786,86.979603069608,87.1898509619374,87.4000988542668,87.6103467465962,87.8205946389256,88.030842531255,88.2410904235844,88.4513383159138,88.6615862082432,88.8718341005726,89.082081992902,89.2923298852314,89.5025777775608,89.7128256698902,89.9230735622196,90.133321454549,90.3435693468784,90.5538172392078,90.7640651315372,90.9743130238666,91.184560916196,91.3948088085254,91.6050567008548,91.8153045931842,92.0255524855136,92.235800377843,92.4460482701724,92.6562961625018,92.8665440548312,93.0767919471606,93.2870398394899,93.4972877318193,93.7075356241487,93.9177835164781,94.1280314088075,94.3382793011369,94.5485271934663,94.7587750857957,94.9690229781251,95.1792708704545,95.3895187627839,95.5997666551133,95.8100145474427,96.0202624397721,96.2305103321015,96.4407582244309,96.6510061167603,96.8612540090897,97.0715019014191,97.2817497937485,97.4919976860779],"text":["age: 52.00000<br />score: 80.88241<br />treatment: no","age: 52.29114<br />score: 81.09266<br />treatment: no","age: 52.58228<br />score: 81.30291<br />treatment: no","age: 52.87342<br />score: 81.51316<br />treatment: no","age: 53.16456<br />score: 81.72341<br />treatment: no","age: 53.45570<br />score: 81.93365<br />treatment: no","age: 53.74684<br />score: 82.14390<br />treatment: no","age: 54.03797<br />score: 82.35415<br />treatment: no","age: 54.32911<br />score: 82.56440<br />treatment: no","age: 54.62025<br />score: 82.77465<br />treatment: no","age: 54.91139<br />score: 82.98489<br />treatment: no","age: 55.20253<br />score: 83.19514<br />treatment: no","age: 55.49367<br />score: 83.40539<br />treatment: no","age: 55.78481<br />score: 83.61564<br />treatment: no","age: 56.07595<br />score: 83.82588<br />treatment: no","age: 56.36709<br />score: 84.03613<br />treatment: no","age: 56.65823<br />score: 84.24638<br />treatment: no","age: 56.94937<br />score: 84.45663<br />treatment: no","age: 57.24051<br />score: 84.66688<br />treatment: no","age: 57.53165<br />score: 84.87712<br />treatment: no","age: 57.82278<br />score: 85.08737<br />treatment: no","age: 58.11392<br />score: 85.29762<br />treatment: no","age: 58.40506<br />score: 85.50787<br />treatment: no","age: 58.69620<br />score: 85.71812<br />treatment: no","age: 58.98734<br />score: 85.92836<br />treatment: no","age: 59.27848<br />score: 86.13861<br />treatment: no","age: 59.56962<br />score: 86.34886<br />treatment: no","age: 59.86076<br />score: 86.55911<br />treatment: no","age: 60.15190<br />score: 86.76936<br />treatment: no","age: 60.44304<br />score: 86.97960<br />treatment: no","age: 60.73418<br />score: 87.18985<br />treatment: no","age: 61.02532<br />score: 87.40010<br />treatment: no","age: 61.31646<br />score: 87.61035<br />treatment: no","age: 61.60759<br />score: 87.82059<br />treatment: no","age: 61.89873<br />score: 88.03084<br />treatment: no","age: 62.18987<br />score: 88.24109<br />treatment: no","age: 62.48101<br />score: 88.45134<br />treatment: no","age: 62.77215<br />score: 88.66159<br />treatment: no","age: 63.06329<br />score: 88.87183<br />treatment: no","age: 63.35443<br />score: 89.08208<br />treatment: no","age: 63.64557<br />score: 89.29233<br />treatment: no","age: 63.93671<br />score: 89.50258<br />treatment: no","age: 64.22785<br />score: 89.71283<br />treatment: no","age: 64.51899<br />score: 89.92307<br />treatment: no","age: 64.81013<br />score: 90.13332<br />treatment: no","age: 65.10127<br />score: 90.34357<br />treatment: no","age: 65.39241<br />score: 90.55382<br />treatment: no","age: 65.68354<br />score: 90.76407<br />treatment: no","age: 65.97468<br />score: 90.97431<br />treatment: no","age: 66.26582<br />score: 91.18456<br />treatment: no","age: 66.55696<br />score: 91.39481<br />treatment: no","age: 66.84810<br />score: 91.60506<br />treatment: no","age: 67.13924<br />score: 91.81530<br />treatment: no","age: 67.43038<br />score: 92.02555<br />treatment: no","age: 67.72152<br />score: 92.23580<br />treatment: no","age: 68.01266<br />score: 92.44605<br />treatment: no","age: 68.30380<br />score: 92.65630<br />treatment: no","age: 68.59494<br />score: 92.86654<br />treatment: no","age: 68.88608<br />score: 93.07679<br />treatment: no","age: 69.17722<br />score: 93.28704<br />treatment: no","age: 69.46835<br />score: 93.49729<br />treatment: no","age: 69.75949<br />score: 93.70754<br />treatment: no","age: 70.05063<br />score: 93.91778<br />treatment: no","age: 70.34177<br />score: 94.12803<br />treatment: no","age: 70.63291<br />score: 94.33828<br />treatment: no","age: 70.92405<br />score: 94.54853<br />treatment: no","age: 71.21519<br />score: 94.75878<br />treatment: no","age: 71.50633<br />score: 94.96902<br />treatment: no","age: 71.79747<br />score: 95.17927<br />treatment: no","age: 72.08861<br />score: 95.38952<br />treatment: no","age: 72.37975<br />score: 95.59977<br />treatment: no","age: 72.67089<br />score: 95.81001<br />treatment: no","age: 72.96203<br />score: 96.02026<br />treatment: no","age: 73.25316<br />score: 96.23051<br />treatment: no","age: 73.54430<br />score: 96.44076<br />treatment: no","age: 73.83544<br />score: 96.65101<br />treatment: no","age: 74.12658<br />score: 96.86125<br />treatment: no","age: 74.41772<br />score: 97.07150<br />treatment: no","age: 74.70886<br />score: 97.28175<br />treatment: no","age: 75.00000<br />score: 97.49200<br />treatment: no"],"type":"scatter","mode":"lines","name":"no","line":{"width":3.77952755905512,"color":"rgba(0,191,196,1)","dash":"solid"},"hoveron":"points","legendgroup":"no","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null}],"layout":{"margin":{"t":28.1765601217656,"r":7.30593607305936,"b":42.130898021309,"l":43.1050228310502},"font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187},"xaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[50.85,76.15],"tickmode":"array","ticktext":["55","60","65","70","75"],"tickvals":[55,60,65,70,75],"categoryorder":"array","categoryarray":["55","60","65","70","75"],"nticks":null,"ticks":"","tickcolor":null,"ticklen":3.65296803652968,"tickwidth":0,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.689497716895},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176,"zeroline":false,"anchor":"y","title":{"text":"age","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"yaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[64.09,101.71],"tickmode":"array","ticktext":["70","80","90","100"],"tickvals":[70,80,90,100],"categoryorder":"array","categoryarray":["70","80","90","100"],"nticks":null,"ticks":"","tickcolor":null,"ticklen":3.65296803652968,"tickwidth":0,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.689497716895},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176,"zeroline":false,"anchor":"x","title":{"text":"score","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"shapes":[{"type":"rect","fillcolor":null,"line":{"color":null,"width":0,"linetype":[]},"yref":"paper","xref":"paper","x0":0,"x1":1,"y0":0,"y1":1}],"showlegend":true,"legend":{"bgcolor":null,"bordercolor":null,"borderwidth":0,"font":{"color":"rgba(0,0,0,1)","family":"","size":11.689497716895},"y":0.927821522309711},"annotations":[{"text":"treatment","x":1.02,"y":1,"showarrow":false,"ax":0,"ay":0,"font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187},"xref":"paper","yref":"paper","textangle":-0,"xanchor":"left","yanchor":"bottom","legendTitle":true}],"hovermode":"closest","barmode":"relative"},"config":{"doubleClick":"reset","showSendToCloud":false},"source":"A","attrs":{"1ecf6ff61cc0":{"x":{},"y":{},"colour":{},"type":"scatter"},"1ecf6d9baad":{"x":{},"y":{},"colour":{}}},"cur_data":"1ecf6ff61cc0","visdat":{"1ecf6ff61cc0":["function (y) ","x"],"1ecf6d9baad":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.2,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- class: inverse, center, middle # Multiple Regression Analysis --- ## The data [Marketing](https://rdrr.io/cran/datarium/man/marketing.html) A data frame containing the impact of three advertising medias (youtube, facebook and newspaper) on sales. Data are the advertising budget in thousands of dollars along with the sales. The advertising experiment has been repeated 200 times. ```r *dat3 <- datarium::marketing dplyr::glimpse(dat3) ``` ``` ## Observations: 200 ## Variables: 4 ## $ youtube <dbl> 276.12, 53.40, 20.64, 181.80, 216.96, 10.44, 69.00, 144.24,… ## $ facebook <dbl> 45.36, 47.16, 55.08, 49.56, 12.96, 58.68, 39.36, 23.52, 2.5… ## $ newspaper <dbl> 83.04, 54.12, 83.16, 70.20, 70.08, 90.00, 28.20, 13.92, 1.2… ## $ sales <dbl> 26.52, 12.48, 11.16, 22.20, 15.48, 8.64, 14.16, 15.84, 5.76… ``` --- ## Fit an additive model Fit an additive regression model using `sales` as dependent variable, and `youtube`as the predictor. -- ``` ## ## Call: ## lm(formula = sales ~ youtube, data = dat3) ## ## Residuals: ## Min 1Q Median 3Q Max ## -10.0632 -2.3454 -0.2295 2.4805 8.6548 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 8.439112 0.549412 15.36 <2e-16 *** ## youtube 0.047537 0.002691 17.67 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 3.91 on 198 degrees of freedom ## Multiple R-squared: 0.6119, Adjusted R-squared: 0.6099 ## F-statistic: 312.1 on 1 and 198 DF, p-value: < 2.2e-16 ``` --- ## Summary: additive model ```r summary(mod_add0)$coefficients ``` ``` ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 8.43911226 0.549411528 15.36028 1.40630e-35 ## youtube 0.04753664 0.002690607 17.66763 1.46739e-42 ``` -- `$$\text{sales} = 8.439 + 0.048 \cdot \text{youtube} + \varepsilon$$` --- ## Fit another additive model Fit another additive regression model using `sales` as dependent variable, and `youtube` and `facebook` as predictors. -- ```r mod_add1 <- lm(sales ~ youtube + facebook, data = dat3) summary(mod_add1) ``` ``` ## ## Call: ## lm(formula = sales ~ youtube + facebook, data = dat3) ## ## Residuals: ## Min 1Q Median 3Q Max ## -10.5572 -1.0502 0.2906 1.4049 3.3994 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 3.50532 0.35339 9.919 <2e-16 *** ## youtube 0.04575 0.00139 32.909 <2e-16 *** ## facebook 0.18799 0.00804 23.382 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 2.018 on 197 degrees of freedom ## Multiple R-squared: 0.8972, Adjusted R-squared: 0.8962 ## F-statistic: 859.6 on 2 and 197 DF, p-value: < 2.2e-16 ``` --- ## Summary: additive model ```r summary(mod_add1)$coefficients ``` ``` ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 3.50531989 0.353387614 9.919193 4.565557e-19 ## youtube 0.04575482 0.001390356 32.908708 5.436980e-82 ## facebook 0.18799423 0.008039973 23.382446 9.776972e-59 ``` -- `$$\text{sales} = 3.505 + 0.046 \cdot \text{youtube} + 0.188 \cdot \text{facebook} + \varepsilon$$` --- ## Visualize: additive model <div id="htmlwidget-16d4d0c4fed3dcb39165" style="width:720px;height:432px;" class="plotly html-widget"></div> <script type="application/json" data-for="htmlwidget-16d4d0c4fed3dcb39165">{"x":{"data":[{"x":[276.12,53.4,20.64,181.8,216.96,10.44,69,144.24,10.32,239.76,79.32,257.64,28.56,117,244.92,234.48,81.36,337.68,83.04,176.76,262.08,284.88,15.84,273.96,74.76,315.48,171.48,288.12,298.56,84.72,351.48,135.48,116.64,318.72,114.84,348.84,320.28,89.64,51.72,273.6,243,212.4,352.32,248.28,30.12,210.12,107.64,287.88,272.64,80.28,239.76,120.48,259.68,219.12,315.24,238.68,8.76,163.44,252.96,252.84,64.2,313.56,287.16,123.24,157.32,82.8,37.8,167.16,284.88,260.16,238.92,131.76,32.16,155.28,256.08,20.28,33,144.6,6.48,139.2,91.68,287.76,90.36,82.08,256.2,231.84,91.56,132.84,105.96,131.76,161.16,34.32,261.24,301.08,128.88,195.96,237.12,221.88,347.64,162.24,266.88,355.68,336.24,225.48,285.84,165.48,30,108.48,15.72,306.48,270.96,290.04,210.84,251.52,93.84,90.12,167.04,91.68,150.84,23.28,169.56,22.56,268.8,147.72,275.4,104.64,9.36,96.24,264.36,71.52,0.84,318.24,10.08,263.76,44.28,57.96,30.72,328.44,51.6,221.88,88.08,232.44,264.6,125.52,115.44,168.36,288.12,291.84,45.6,53.64,336.84,145.2,237.12,205.56,225.36,4.92,112.68,179.76,14.04,158.04,207,102.84,226.08,196.2,140.64,281.4,21.48,248.16,258.48,341.16,60,197.4,23.52,202.08,266.88,332.28,298.08,204.24,332.04,198.72,187.92,262.2,67.44,345.12,304.56,246,167.4,229.32,343.2,22.44,47.4,90.6,20.64,200.16,179.64,45.84,113.04,212.4,340.32,278.52],"y":[26.52,12.48,11.16,22.2,15.48,8.64,14.16,15.84,5.76,12.72,10.32,20.88,11.04,11.64,22.8,26.88,15,29.28,13.56,17.52,21.6,15,6.72,18.6,11.64,14.4,18,19.08,22.68,12.6,25.68,14.28,11.52,20.88,11.4,15.36,30.48,17.64,12.12,25.8,19.92,20.52,24.84,15.48,10.2,17.88,12.72,27.84,17.76,11.64,13.68,12.84,27.12,25.44,24.24,28.44,6.6,15.84,28.56,22.08,9.72,29.04,18.84,16.8,21.6,11.16,11.4,16.08,22.68,26.76,21.96,14.88,10.56,13.2,20.4,10.44,8.28,17.04,6.36,13.2,14.16,14.76,13.56,16.32,26.04,18.24,14.4,19.2,15.48,20.04,13.44,8.76,23.28,26.64,13.8,20.28,14.04,18.6,30.48,20.64,14.04,28.56,17.76,17.64,24.84,23.04,8.64,10.44,6.36,23.76,16.08,26.16,16.92,19.08,17.52,15.12,14.64,11.28,19.08,7.92,18.6,8.4,13.92,18.24,23.64,12.72,7.92,10.56,29.64,11.64,1.92,15.24,6.84,23.52,12.96,13.92,11.4,24.96,11.52,24.84,13.08,23.04,24.12,12.48,13.68,12.36,15.84,30.48,13.08,12.12,19.32,13.92,19.92,22.8,18.72,3.84,18.36,12.12,8.76,15.48,17.28,15.96,17.88,21.6,14.28,14.28,9.6,14.64,20.52,18,10.08,17.4,9.12,14.04,13.8,32.4,24.24,14.04,14.16,15.12,12.6,14.64,10.44,31.44,21.12,27.12,12.36,20.76,19.08,8.04,12.96,11.88,7.08,23.52,20.76,9.12,11.64,15.36,30.6,16.08],"text":["youtube: 276.12<br />sales: 26.52<br />facebook: 45.36","youtube: 53.40<br />sales: 12.48<br />facebook: 47.16","youtube: 20.64<br />sales: 11.16<br />facebook: 55.08","youtube: 181.80<br />sales: 22.20<br />facebook: 49.56","youtube: 216.96<br />sales: 15.48<br />facebook: 12.96","youtube: 10.44<br />sales: 8.64<br />facebook: 58.68","youtube: 69.00<br />sales: 14.16<br />facebook: 39.36","youtube: 144.24<br />sales: 15.84<br />facebook: 23.52","youtube: 10.32<br />sales: 5.76<br />facebook: 2.52","youtube: 239.76<br />sales: 12.72<br />facebook: 3.12","youtube: 79.32<br />sales: 10.32<br />facebook: 6.96","youtube: 257.64<br />sales: 20.88<br />facebook: 28.80","youtube: 28.56<br />sales: 11.04<br />facebook: 42.12","youtube: 117.00<br />sales: 11.64<br />facebook: 9.12","youtube: 244.92<br />sales: 22.80<br />facebook: 39.48","youtube: 234.48<br />sales: 26.88<br />facebook: 57.24","youtube: 81.36<br />sales: 15.00<br />facebook: 43.92","youtube: 337.68<br />sales: 29.28<br />facebook: 47.52","youtube: 83.04<br />sales: 13.56<br />facebook: 24.60","youtube: 176.76<br />sales: 17.52<br />facebook: 28.68","youtube: 262.08<br />sales: 21.60<br />facebook: 33.24","youtube: 284.88<br />sales: 15.00<br />facebook: 6.12","youtube: 15.84<br />sales: 6.72<br />facebook: 19.08","youtube: 273.96<br />sales: 18.60<br />facebook: 20.28","youtube: 74.76<br />sales: 11.64<br />facebook: 15.12","youtube: 315.48<br />sales: 14.40<br />facebook: 4.20","youtube: 171.48<br />sales: 18.00<br />facebook: 35.16","youtube: 288.12<br />sales: 19.08<br />facebook: 20.04","youtube: 298.56<br />sales: 22.68<br />facebook: 32.52","youtube: 84.72<br />sales: 12.60<br />facebook: 19.20","youtube: 351.48<br />sales: 25.68<br />facebook: 33.96","youtube: 135.48<br />sales: 14.28<br />facebook: 20.88","youtube: 116.64<br />sales: 11.52<br />facebook: 1.80","youtube: 318.72<br />sales: 20.88<br />facebook: 24.00","youtube: 114.84<br />sales: 11.40<br />facebook: 1.68","youtube: 348.84<br />sales: 15.36<br />facebook: 4.92","youtube: 320.28<br />sales: 30.48<br />facebook: 52.56","youtube: 89.64<br />sales: 17.64<br />facebook: 59.28","youtube: 51.72<br />sales: 12.12<br />facebook: 32.04","youtube: 273.60<br />sales: 25.80<br />facebook: 45.24","youtube: 243.00<br />sales: 19.92<br />facebook: 26.76","youtube: 212.40<br />sales: 20.52<br />facebook: 40.08","youtube: 352.32<br />sales: 24.84<br />facebook: 33.24","youtube: 248.28<br />sales: 15.48<br />facebook: 10.08","youtube: 30.12<br />sales: 10.20<br />facebook: 30.84","youtube: 210.12<br />sales: 17.88<br />facebook: 27.00","youtube: 107.64<br />sales: 12.72<br />facebook: 11.88","youtube: 287.88<br />sales: 27.84<br />facebook: 49.80","youtube: 272.64<br />sales: 17.76<br />facebook: 18.96","youtube: 80.28<br />sales: 11.64<br />facebook: 14.04","youtube: 239.76<br />sales: 13.68<br />facebook: 3.72","youtube: 120.48<br />sales: 12.84<br />facebook: 11.52","youtube: 259.68<br />sales: 27.12<br />facebook: 50.04","youtube: 219.12<br />sales: 25.44<br />facebook: 55.44","youtube: 315.24<br />sales: 24.24<br />facebook: 34.56","youtube: 238.68<br />sales: 28.44<br />facebook: 59.28","youtube: 8.76<br />sales: 6.60<br />facebook: 33.72","youtube: 163.44<br />sales: 15.84<br />facebook: 23.04","youtube: 252.96<br />sales: 28.56<br />facebook: 59.52","youtube: 252.84<br />sales: 22.08<br />facebook: 35.40","youtube: 64.20<br />sales: 9.72<br />facebook: 2.40","youtube: 313.56<br />sales: 29.04<br />facebook: 51.24","youtube: 287.16<br />sales: 18.84<br />facebook: 18.60","youtube: 123.24<br />sales: 16.80<br />facebook: 35.52","youtube: 157.32<br />sales: 21.60<br />facebook: 51.36","youtube: 82.80<br />sales: 11.16<br />facebook: 11.16","youtube: 37.80<br />sales: 11.40<br />facebook: 29.52","youtube: 167.16<br />sales: 16.08<br />facebook: 17.40","youtube: 284.88<br />sales: 22.68<br />facebook: 33.00","youtube: 260.16<br />sales: 26.76<br />facebook: 52.68","youtube: 238.92<br />sales: 21.96<br />facebook: 36.72","youtube: 131.76<br />sales: 14.88<br />facebook: 17.16","youtube: 32.16<br />sales: 10.56<br />facebook: 39.60","youtube: 155.28<br />sales: 13.20<br />facebook: 6.84","youtube: 256.08<br />sales: 20.40<br />facebook: 29.52","youtube: 20.28<br />sales: 10.44<br />facebook: 52.44","youtube: 33.00<br />sales: 8.28<br />facebook: 1.92","youtube: 144.60<br />sales: 17.04<br />facebook: 34.20","youtube: 6.48<br />sales: 6.36<br />facebook: 35.88","youtube: 139.20<br />sales: 13.20<br />facebook: 9.24","youtube: 91.68<br />sales: 14.16<br />facebook: 32.04","youtube: 287.76<br />sales: 14.76<br />facebook: 4.92","youtube: 90.36<br />sales: 13.56<br />facebook: 24.36","youtube: 82.08<br />sales: 16.32<br />facebook: 53.40","youtube: 256.20<br />sales: 26.04<br />facebook: 51.60","youtube: 231.84<br />sales: 18.24<br />facebook: 22.08","youtube: 91.56<br />sales: 14.40<br />facebook: 33.00","youtube: 132.84<br />sales: 19.20<br />facebook: 48.72","youtube: 105.96<br />sales: 15.48<br />facebook: 30.60","youtube: 131.76<br />sales: 20.04<br />facebook: 57.36","youtube: 161.16<br />sales: 13.44<br />facebook: 5.88","youtube: 34.32<br />sales: 8.76<br />facebook: 1.80","youtube: 261.24<br />sales: 23.28<br />facebook: 40.20","youtube: 301.08<br />sales: 26.64<br />facebook: 43.80","youtube: 128.88<br />sales: 13.80<br />facebook: 16.80","youtube: 195.96<br />sales: 20.28<br />facebook: 37.92","youtube: 237.12<br />sales: 14.04<br />facebook: 4.20","youtube: 221.88<br />sales: 18.60<br />facebook: 25.20","youtube: 347.64<br />sales: 30.48<br />facebook: 50.76","youtube: 162.24<br />sales: 20.64<br />facebook: 50.04","youtube: 266.88<br />sales: 14.04<br />facebook: 5.16","youtube: 355.68<br />sales: 28.56<br />facebook: 43.56","youtube: 336.24<br />sales: 17.76<br />facebook: 12.12","youtube: 225.48<br />sales: 17.64<br />facebook: 20.64","youtube: 285.84<br />sales: 24.84<br />facebook: 41.16","youtube: 165.48<br />sales: 23.04<br />facebook: 55.68","youtube: 30.00<br />sales: 8.64<br />facebook: 13.20","youtube: 108.48<br />sales: 10.44<br />facebook: 0.36","youtube: 15.72<br />sales: 6.36<br />facebook: 0.48","youtube: 306.48<br />sales: 23.76<br />facebook: 32.28","youtube: 270.96<br />sales: 16.08<br />facebook: 9.84","youtube: 290.04<br />sales: 26.16<br />facebook: 45.60","youtube: 210.84<br />sales: 16.92<br />facebook: 18.48","youtube: 251.52<br />sales: 19.08<br />facebook: 24.72","youtube: 93.84<br />sales: 17.52<br />facebook: 56.16","youtube: 90.12<br />sales: 15.12<br />facebook: 42.00","youtube: 167.04<br />sales: 14.64<br />facebook: 17.16","youtube: 91.68<br />sales: 11.28<br />facebook: 0.96","youtube: 150.84<br />sales: 19.08<br />facebook: 44.28","youtube: 23.28<br />sales: 7.92<br />facebook: 19.20","youtube: 169.56<br />sales: 18.60<br />facebook: 32.16","youtube: 22.56<br />sales: 8.40<br />facebook: 26.04","youtube: 268.80<br />sales: 13.92<br />facebook: 2.88","youtube: 147.72<br />sales: 18.24<br />facebook: 41.52","youtube: 275.40<br />sales: 23.64<br />facebook: 38.76","youtube: 104.64<br />sales: 12.72<br />facebook: 14.16","youtube: 9.36<br />sales: 7.92<br />facebook: 46.68","youtube: 96.24<br />sales: 10.56<br />facebook: 0.00","youtube: 264.36<br />sales: 29.64<br />facebook: 58.80","youtube: 71.52<br />sales: 11.64<br />facebook: 14.40","youtube: 0.84<br />sales: 1.92<br />facebook: 47.52","youtube: 318.24<br />sales: 15.24<br />facebook: 3.48","youtube: 10.08<br />sales: 6.84<br />facebook: 32.64","youtube: 263.76<br />sales: 23.52<br />facebook: 40.20","youtube: 44.28<br />sales: 12.96<br />facebook: 46.32","youtube: 57.96<br />sales: 13.92<br />facebook: 56.40","youtube: 30.72<br />sales: 11.40<br />facebook: 46.80","youtube: 328.44<br />sales: 24.96<br />facebook: 34.68","youtube: 51.60<br />sales: 11.52<br />facebook: 31.08","youtube: 221.88<br />sales: 24.84<br />facebook: 52.68","youtube: 88.08<br />sales: 13.08<br />facebook: 20.40","youtube: 232.44<br />sales: 23.04<br />facebook: 42.48","youtube: 264.60<br />sales: 24.12<br />facebook: 39.84","youtube: 125.52<br />sales: 12.48<br />facebook: 6.84","youtube: 115.44<br />sales: 13.68<br />facebook: 17.76","youtube: 168.36<br />sales: 12.36<br />facebook: 2.28","youtube: 288.12<br />sales: 15.84<br />facebook: 8.76","youtube: 291.84<br />sales: 30.48<br />facebook: 58.80","youtube: 45.60<br />sales: 13.08<br />facebook: 48.36","youtube: 53.64<br />sales: 12.12<br />facebook: 30.96","youtube: 336.84<br />sales: 19.32<br />facebook: 16.68","youtube: 145.20<br />sales: 13.92<br />facebook: 10.08","youtube: 237.12<br />sales: 19.92<br />facebook: 27.96","youtube: 205.56<br />sales: 22.80<br />facebook: 47.64","youtube: 225.36<br />sales: 18.72<br />facebook: 25.32","youtube: 4.92<br />sales: 3.84<br />facebook: 13.92","youtube: 112.68<br />sales: 18.36<br />facebook: 52.20","youtube: 179.76<br />sales: 12.12<br />facebook: 1.56","youtube: 14.04<br />sales: 8.76<br />facebook: 44.28","youtube: 158.04<br />sales: 15.48<br />facebook: 22.08","youtube: 207.00<br />sales: 17.28<br />facebook: 21.72","youtube: 102.84<br />sales: 15.96<br />facebook: 42.96","youtube: 226.08<br />sales: 17.88<br />facebook: 21.72","youtube: 196.20<br />sales: 21.60<br />facebook: 44.16","youtube: 140.64<br />sales: 14.28<br />facebook: 17.64","youtube: 281.40<br />sales: 14.28<br />facebook: 4.08","youtube: 21.48<br />sales: 9.60<br />facebook: 45.12","youtube: 248.16<br />sales: 14.64<br />facebook: 6.24","youtube: 258.48<br />sales: 20.52<br />facebook: 28.32","youtube: 341.16<br />sales: 18.00<br />facebook: 12.72","youtube: 60.00<br />sales: 10.08<br />facebook: 13.92","youtube: 197.40<br />sales: 17.40<br />facebook: 25.08","youtube: 23.52<br />sales: 9.12<br />facebook: 24.12","youtube: 202.08<br />sales: 14.04<br />facebook: 8.52","youtube: 266.88<br />sales: 13.80<br />facebook: 4.08","youtube: 332.28<br />sales: 32.40<br />facebook: 58.68","youtube: 298.08<br />sales: 24.24<br />facebook: 36.24","youtube: 204.24<br />sales: 14.04<br />facebook: 9.36","youtube: 332.04<br />sales: 14.16<br />facebook: 2.76","youtube: 198.72<br />sales: 15.12<br />facebook: 12.00","youtube: 187.92<br />sales: 12.60<br />facebook: 3.12","youtube: 262.20<br />sales: 14.64<br />facebook: 6.48","youtube: 67.44<br />sales: 10.44<br />facebook: 6.84","youtube: 345.12<br />sales: 31.44<br />facebook: 51.60","youtube: 304.56<br />sales: 21.12<br />facebook: 25.56","youtube: 246.00<br />sales: 27.12<br />facebook: 54.12","youtube: 167.40<br />sales: 12.36<br />facebook: 2.52","youtube: 229.32<br />sales: 20.76<br />facebook: 34.44","youtube: 343.20<br />sales: 19.08<br />facebook: 16.68","youtube: 22.44<br />sales: 8.04<br />facebook: 14.52","youtube: 47.40<br />sales: 12.96<br />facebook: 49.32","youtube: 90.60<br />sales: 11.88<br />facebook: 12.96","youtube: 20.64<br />sales: 7.08<br />facebook: 4.92","youtube: 200.16<br />sales: 23.52<br />facebook: 50.40","youtube: 179.64<br />sales: 20.76<br />facebook: 42.72","youtube: 45.84<br />sales: 9.12<br />facebook: 4.44","youtube: 113.04<br />sales: 11.64<br />facebook: 5.88","youtube: 212.40<br />sales: 15.36<br />facebook: 11.16","youtube: 340.32<br />sales: 30.60<br />facebook: 50.40","youtube: 278.52<br />sales: 16.08<br />facebook: 10.32"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":["rgba(69,142,201,1)","rgba(71,147,206,1)","rgba(81,166,232,1)","rgba(74,153,214,1)","rgba(32,69,103,1)","rgba(85,175,244,1)","rgba(62,128,182,1)","rgba(44,92,133,1)","rgba(22,48,74,1)","rgba(22,49,75,1)","rgba(26,57,86,1)","rgba(50,104,149,1)","rgba(65,135,190,1)","rgba(28,61,92,1)","rgba(62,129,182,1)","rgba(83,171,239,1)","rgba(67,139,196,1)","rgba(71,148,208,1)","rgba(45,95,136,1)","rgba(50,104,149,1)","rgba(55,114,163,1)","rgba(25,55,83,1)","rgba(39,82,120,1)","rgba(40,85,124,1)","rgba(35,74,109,1)","rgba(23,51,78,1)","rgba(57,118,169,1)","rgba(40,85,123,1)","rgba(54,112,160,1)","rgba(39,83,120,1)","rgba(56,116,165,1)","rgba(41,86,125,1)","rgba(21,47,72,1)","rgba(44,93,135,1)","rgba(21,46,71,1)","rgba(24,53,80,1)","rgba(78,160,224,1)","rgba(86,176,246,1)","rgba(53,111,159,1)","rgba(69,142,200,1)","rgba(47,99,143,1)","rgba(63,130,184,1)","rgba(55,114,163,1)","rgba(29,63,94,1)","rgba(52,109,155,1)","rgba(48,100,144,1)","rgba(31,67,99,1)","rgba(74,153,215,1)","rgba(39,82,120,1)","rgba(33,72,106,1)","rgba(23,50,77,1)","rgba(31,66,98,1)","rgba(74,154,216,1)","rgba(81,167,233,1)","rgba(56,117,167,1)","rgba(86,176,246,1)","rgba(55,115,164,1)","rgba(43,91,132,1)","rgba(86,177,247,1)","rgba(57,119,169,1)","rgba(21,48,73,1)","rgba(76,157,220,1)","rgba(38,81,119,1)","rgba(57,119,170,1)","rgba(76,157,220,1)","rgba(30,66,97,1)","rgba(51,106,151,1)","rgba(37,79,115,1)","rgba(54,114,162,1)","rgba(78,160,224,1)","rgba(59,122,173,1)","rgba(37,78,115,1)","rgba(62,129,182,1)","rgba(26,57,85,1)","rgba(51,106,151,1)","rgba(77,160,224,1)","rgba(21,47,72,1)","rgba(56,116,166,1)","rgba(58,120,171,1)","rgba(28,62,92,1)","rgba(53,111,159,1)","rgba(24,53,80,1)","rgba(45,94,136,1)","rgba(79,162,227,1)","rgba(76,158,221,1)","rgba(42,89,129,1)","rgba(54,114,162,1)","rgba(73,151,212,1)","rgba(52,108,155,1)","rgba(83,172,240,1)","rgba(25,55,83,1)","rgba(21,47,72,1)","rgba(63,130,184,1)","rgba(67,139,196,1)","rgba(36,78,113,1)","rgba(60,125,177,1)","rgba(23,51,78,1)","rgba(46,96,138,1)","rgba(75,155,218,1)","rgba(74,154,216,1)","rgba(24,53,81,1)","rgba(67,138,195,1)","rgba(31,68,100,1)","rgba(41,86,125,1)","rgba(64,132,187,1)","rgba(81,168,234,1)","rgba(33,70,103,1)","rgba(19,44,68,1)","rgba(19,44,68,1)","rgba(54,112,160,1)","rgba(29,63,94,1)","rgba(69,143,201,1)","rgba(38,81,118,1)","rgba(45,95,137,1)","rgba(82,169,236,1)","rgba(65,134,190,1)","rgba(37,78,115,1)","rgba(20,45,70,1)","rgba(68,140,197,1)","rgba(39,83,120,1)","rgba(54,112,159,1)","rgba(47,98,141,1)","rgba(22,49,75,1)","rgba(64,133,188,1)","rgba(61,127,180,1)","rgba(34,72,106,1)","rgba(70,146,205,1)","rgba(19,43,67,1)","rgba(85,175,245,1)","rgba(34,72,107,1)","rgba(71,148,208,1)","rgba(23,50,76,1)","rgba(54,113,161,1)","rgba(63,130,184,1)","rgba(70,145,204,1)","rgba(82,169,237,1)","rgba(71,146,205,1)","rgba(56,117,167,1)","rgba(52,109,156,1)","rgba(78,160,224,1)","rgba(40,85,124,1)","rgba(65,136,192,1)","rgba(62,129,183,1)","rgba(26,57,85,1)","rgba(37,80,116,1)","rgba(21,47,73,1)","rgba(28,61,91,1)","rgba(85,175,245,1)","rgba(72,150,210,1)","rgba(52,109,156,1)","rgba(36,77,113,1)","rgba(29,63,94,1)","rgba(49,102,146,1)","rgba(72,148,208,1)","rgba(46,96,139,1)","rgba(33,71,105,1)","rgba(77,159,223,1)","rgba(21,46,71,1)","rgba(68,140,197,1)","rgba(42,89,129,1)","rgba(42,88,128,1)","rgba(66,137,193,1)","rgba(42,88,128,1)","rgba(67,140,197,1)","rgba(37,79,116,1)","rgba(23,51,78,1)","rgba(69,142,200,1)","rgba(25,55,84,1)","rgba(49,103,148,1)","rgba(32,69,102,1)","rgba(33,71,105,1)","rgba(46,96,138,1)","rgba(44,93,135,1)","rgba(28,60,90,1)","rgba(23,51,78,1)","rgba(85,175,244,1)","rgba(58,121,172,1)","rgba(29,62,92,1)","rgba(22,48,74,1)","rgba(31,67,100,1)","rgba(22,49,75,1)","rgba(26,56,84,1)","rgba(26,57,85,1)","rgba(76,158,221,1)","rgba(46,97,139,1)","rgba(79,164,229,1)","rgba(22,48,74,1)","rgba(56,117,166,1)","rgba(36,77,113,1)","rgba(34,73,107,1)","rgba(74,152,213,1)","rgba(32,69,103,1)","rgba(24,53,80,1)","rgba(75,155,217,1)","rgba(66,136,192,1)","rgba(23,52,79,1)","rgba(25,55,83,1)","rgba(30,66,97,1)","rgba(75,155,217,1)","rgba(30,64,95,1)"],"opacity":1,"size":5.66929133858268,"symbol":"circle","line":{"width":1.88976377952756,"color":["rgba(69,142,201,1)","rgba(71,147,206,1)","rgba(81,166,232,1)","rgba(74,153,214,1)","rgba(32,69,103,1)","rgba(85,175,244,1)","rgba(62,128,182,1)","rgba(44,92,133,1)","rgba(22,48,74,1)","rgba(22,49,75,1)","rgba(26,57,86,1)","rgba(50,104,149,1)","rgba(65,135,190,1)","rgba(28,61,92,1)","rgba(62,129,182,1)","rgba(83,171,239,1)","rgba(67,139,196,1)","rgba(71,148,208,1)","rgba(45,95,136,1)","rgba(50,104,149,1)","rgba(55,114,163,1)","rgba(25,55,83,1)","rgba(39,82,120,1)","rgba(40,85,124,1)","rgba(35,74,109,1)","rgba(23,51,78,1)","rgba(57,118,169,1)","rgba(40,85,123,1)","rgba(54,112,160,1)","rgba(39,83,120,1)","rgba(56,116,165,1)","rgba(41,86,125,1)","rgba(21,47,72,1)","rgba(44,93,135,1)","rgba(21,46,71,1)","rgba(24,53,80,1)","rgba(78,160,224,1)","rgba(86,176,246,1)","rgba(53,111,159,1)","rgba(69,142,200,1)","rgba(47,99,143,1)","rgba(63,130,184,1)","rgba(55,114,163,1)","rgba(29,63,94,1)","rgba(52,109,155,1)","rgba(48,100,144,1)","rgba(31,67,99,1)","rgba(74,153,215,1)","rgba(39,82,120,1)","rgba(33,72,106,1)","rgba(23,50,77,1)","rgba(31,66,98,1)","rgba(74,154,216,1)","rgba(81,167,233,1)","rgba(56,117,167,1)","rgba(86,176,246,1)","rgba(55,115,164,1)","rgba(43,91,132,1)","rgba(86,177,247,1)","rgba(57,119,169,1)","rgba(21,48,73,1)","rgba(76,157,220,1)","rgba(38,81,119,1)","rgba(57,119,170,1)","rgba(76,157,220,1)","rgba(30,66,97,1)","rgba(51,106,151,1)","rgba(37,79,115,1)","rgba(54,114,162,1)","rgba(78,160,224,1)","rgba(59,122,173,1)","rgba(37,78,115,1)","rgba(62,129,182,1)","rgba(26,57,85,1)","rgba(51,106,151,1)","rgba(77,160,224,1)","rgba(21,47,72,1)","rgba(56,116,166,1)","rgba(58,120,171,1)","rgba(28,62,92,1)","rgba(53,111,159,1)","rgba(24,53,80,1)","rgba(45,94,136,1)","rgba(79,162,227,1)","rgba(76,158,221,1)","rgba(42,89,129,1)","rgba(54,114,162,1)","rgba(73,151,212,1)","rgba(52,108,155,1)","rgba(83,172,240,1)","rgba(25,55,83,1)","rgba(21,47,72,1)","rgba(63,130,184,1)","rgba(67,139,196,1)","rgba(36,78,113,1)","rgba(60,125,177,1)","rgba(23,51,78,1)","rgba(46,96,138,1)","rgba(75,155,218,1)","rgba(74,154,216,1)","rgba(24,53,81,1)","rgba(67,138,195,1)","rgba(31,68,100,1)","rgba(41,86,125,1)","rgba(64,132,187,1)","rgba(81,168,234,1)","rgba(33,70,103,1)","rgba(19,44,68,1)","rgba(19,44,68,1)","rgba(54,112,160,1)","rgba(29,63,94,1)","rgba(69,143,201,1)","rgba(38,81,118,1)","rgba(45,95,137,1)","rgba(82,169,236,1)","rgba(65,134,190,1)","rgba(37,78,115,1)","rgba(20,45,70,1)","rgba(68,140,197,1)","rgba(39,83,120,1)","rgba(54,112,159,1)","rgba(47,98,141,1)","rgba(22,49,75,1)","rgba(64,133,188,1)","rgba(61,127,180,1)","rgba(34,72,106,1)","rgba(70,146,205,1)","rgba(19,43,67,1)","rgba(85,175,245,1)","rgba(34,72,107,1)","rgba(71,148,208,1)","rgba(23,50,76,1)","rgba(54,113,161,1)","rgba(63,130,184,1)","rgba(70,145,204,1)","rgba(82,169,237,1)","rgba(71,146,205,1)","rgba(56,117,167,1)","rgba(52,109,156,1)","rgba(78,160,224,1)","rgba(40,85,124,1)","rgba(65,136,192,1)","rgba(62,129,183,1)","rgba(26,57,85,1)","rgba(37,80,116,1)","rgba(21,47,73,1)","rgba(28,61,91,1)","rgba(85,175,245,1)","rgba(72,150,210,1)","rgba(52,109,156,1)","rgba(36,77,113,1)","rgba(29,63,94,1)","rgba(49,102,146,1)","rgba(72,148,208,1)","rgba(46,96,139,1)","rgba(33,71,105,1)","rgba(77,159,223,1)","rgba(21,46,71,1)","rgba(68,140,197,1)","rgba(42,89,129,1)","rgba(42,88,128,1)","rgba(66,137,193,1)","rgba(42,88,128,1)","rgba(67,140,197,1)","rgba(37,79,116,1)","rgba(23,51,78,1)","rgba(69,142,200,1)","rgba(25,55,84,1)","rgba(49,103,148,1)","rgba(32,69,102,1)","rgba(33,71,105,1)","rgba(46,96,138,1)","rgba(44,93,135,1)","rgba(28,60,90,1)","rgba(23,51,78,1)","rgba(85,175,244,1)","rgba(58,121,172,1)","rgba(29,62,92,1)","rgba(22,48,74,1)","rgba(31,67,100,1)","rgba(22,49,75,1)","rgba(26,56,84,1)","rgba(26,57,85,1)","rgba(76,158,221,1)","rgba(46,97,139,1)","rgba(79,164,229,1)","rgba(22,48,74,1)","rgba(56,117,166,1)","rgba(36,77,113,1)","rgba(34,73,107,1)","rgba(74,152,213,1)","rgba(32,69,103,1)","rgba(24,53,80,1)","rgba(75,155,217,1)","rgba(66,136,192,1)","rgba(23,52,79,1)","rgba(25,55,83,1)","rgba(30,66,97,1)","rgba(75,155,217,1)","rgba(30,64,95,1)"]}},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[0.84,5.33164556962025,9.8232911392405,14.3149367088608,18.806582278481,23.2982278481013,27.7898734177215,32.2815189873418,36.773164556962,41.2648101265823,45.7564556962025,50.2481012658228,54.739746835443,59.2313924050633,63.7230379746835,68.2146835443038,72.706329113924,77.1979746835443,81.6896202531645,86.1812658227848,90.6729113924051,95.1645569620253,99.6562025316456,104.147848101266,108.639493670886,113.131139240506,117.622784810127,122.114430379747,126.606075949367,131.097721518987,135.589367088608,140.081012658228,144.572658227848,149.064303797468,153.555949367089,158.047594936709,162.539240506329,167.030886075949,171.52253164557,176.01417721519,180.50582278481,184.99746835443,189.489113924051,193.980759493671,198.472405063291,202.964050632911,207.455696202532,211.947341772152,216.438987341772,220.930632911392,225.422278481013,229.913924050633,234.405569620253,238.897215189873,243.388860759494,247.880506329114,252.372151898734,256.863797468354,261.355443037975,265.847088607595,270.338734177215,274.830379746835,279.322025316456,283.813670886076,288.305316455696,292.796962025316,297.288607594937,301.780253164557,306.271898734177,310.763544303797,315.255189873418,319.746835443038,324.238481012658,328.730126582278,333.221772151899,337.713417721519,342.205063291139,346.696708860759,351.18835443038,355.68],"y":[8.47904303691697,8.69256077731257,8.90607851770818,9.11959625810378,9.33311399849939,9.54663173889499,9.76014947929059,9.9736672196862,10.1871849600818,10.4007027004774,10.614220440873,10.8277381812686,11.0412559216642,11.2547736620598,11.4682914024554,11.681809142851,11.8953268832466,12.1088446236422,12.3223623640378,12.5358801044334,12.7493978448291,12.9629155852247,13.1764333256203,13.3899510660159,13.6034688064115,13.8169865468071,14.0305042872027,14.2440220275983,14.4575397679939,14.6710575083895,14.8845752487851,15.0980929891807,15.3116107295763,15.5251284699719,15.7386462103675,15.9521639507631,16.1656816911587,16.3791994315543,16.5927171719499,16.8062349123455,17.0197526527411,17.2332703931367,17.4467881335323,17.6603058739279,17.8738236143236,18.0873413547192,18.3008590951148,18.5143768355104,18.727894575906,18.9414123163016,19.1549300566972,19.3684477970928,19.5819655374884,19.795483277884,20.0090010182796,20.2225187586752,20.4360364990708,20.6495542394664,20.863071979862,21.0765897202576,21.2901074606532,21.5036252010488,21.7171429414444,21.93066068184,22.1441784222356,22.3576961626312,22.5712139030268,22.7847316434224,22.998249383818,23.2117671242137,23.4252848646093,23.6388026050049,23.8523203454005,24.0658380857961,24.2793558261917,24.4928735665873,24.7063913069829,24.9199090473785,25.1334267877741,25.3469445281697],"text":["youtube: 0.840000<br />sales: 8.479043<br />facebook: #3366FF","youtube: 5.331646<br />sales: 8.692561<br />facebook: #3366FF","youtube: 9.823291<br />sales: 8.906079<br />facebook: #3366FF","youtube: 14.314937<br />sales: 9.119596<br />facebook: #3366FF","youtube: 18.806582<br />sales: 9.333114<br />facebook: #3366FF","youtube: 23.298228<br />sales: 9.546632<br />facebook: #3366FF","youtube: 27.789873<br />sales: 9.760149<br />facebook: #3366FF","youtube: 32.281519<br />sales: 9.973667<br />facebook: #3366FF","youtube: 36.773165<br />sales: 10.187185<br />facebook: #3366FF","youtube: 41.264810<br />sales: 10.400703<br />facebook: #3366FF","youtube: 45.756456<br />sales: 10.614220<br />facebook: #3366FF","youtube: 50.248101<br />sales: 10.827738<br />facebook: #3366FF","youtube: 54.739747<br />sales: 11.041256<br />facebook: #3366FF","youtube: 59.231392<br />sales: 11.254774<br />facebook: #3366FF","youtube: 63.723038<br />sales: 11.468291<br />facebook: #3366FF","youtube: 68.214684<br />sales: 11.681809<br />facebook: #3366FF","youtube: 72.706329<br />sales: 11.895327<br />facebook: #3366FF","youtube: 77.197975<br />sales: 12.108845<br />facebook: #3366FF","youtube: 81.689620<br />sales: 12.322362<br />facebook: #3366FF","youtube: 86.181266<br />sales: 12.535880<br />facebook: #3366FF","youtube: 90.672911<br />sales: 12.749398<br />facebook: #3366FF","youtube: 95.164557<br />sales: 12.962916<br />facebook: #3366FF","youtube: 99.656203<br />sales: 13.176433<br />facebook: #3366FF","youtube: 104.147848<br />sales: 13.389951<br />facebook: #3366FF","youtube: 108.639494<br />sales: 13.603469<br />facebook: #3366FF","youtube: 113.131139<br />sales: 13.816987<br />facebook: #3366FF","youtube: 117.622785<br />sales: 14.030504<br />facebook: #3366FF","youtube: 122.114430<br />sales: 14.244022<br />facebook: #3366FF","youtube: 126.606076<br />sales: 14.457540<br />facebook: #3366FF","youtube: 131.097722<br />sales: 14.671058<br />facebook: #3366FF","youtube: 135.589367<br />sales: 14.884575<br />facebook: #3366FF","youtube: 140.081013<br />sales: 15.098093<br />facebook: #3366FF","youtube: 144.572658<br />sales: 15.311611<br />facebook: #3366FF","youtube: 149.064304<br />sales: 15.525128<br />facebook: #3366FF","youtube: 153.555949<br />sales: 15.738646<br />facebook: #3366FF","youtube: 158.047595<br />sales: 15.952164<br />facebook: #3366FF","youtube: 162.539241<br />sales: 16.165682<br />facebook: #3366FF","youtube: 167.030886<br />sales: 16.379199<br />facebook: #3366FF","youtube: 171.522532<br />sales: 16.592717<br />facebook: #3366FF","youtube: 176.014177<br />sales: 16.806235<br />facebook: #3366FF","youtube: 180.505823<br />sales: 17.019753<br />facebook: #3366FF","youtube: 184.997468<br />sales: 17.233270<br />facebook: #3366FF","youtube: 189.489114<br />sales: 17.446788<br />facebook: #3366FF","youtube: 193.980759<br />sales: 17.660306<br />facebook: #3366FF","youtube: 198.472405<br />sales: 17.873824<br />facebook: #3366FF","youtube: 202.964051<br />sales: 18.087341<br />facebook: #3366FF","youtube: 207.455696<br />sales: 18.300859<br />facebook: #3366FF","youtube: 211.947342<br />sales: 18.514377<br />facebook: #3366FF","youtube: 216.438987<br />sales: 18.727895<br />facebook: #3366FF","youtube: 220.930633<br />sales: 18.941412<br />facebook: #3366FF","youtube: 225.422278<br />sales: 19.154930<br />facebook: #3366FF","youtube: 229.913924<br />sales: 19.368448<br />facebook: #3366FF","youtube: 234.405570<br />sales: 19.581966<br />facebook: #3366FF","youtube: 238.897215<br />sales: 19.795483<br />facebook: #3366FF","youtube: 243.388861<br />sales: 20.009001<br />facebook: #3366FF","youtube: 247.880506<br />sales: 20.222519<br />facebook: #3366FF","youtube: 252.372152<br />sales: 20.436036<br />facebook: #3366FF","youtube: 256.863797<br />sales: 20.649554<br />facebook: #3366FF","youtube: 261.355443<br />sales: 20.863072<br />facebook: #3366FF","youtube: 265.847089<br />sales: 21.076590<br />facebook: #3366FF","youtube: 270.338734<br />sales: 21.290107<br />facebook: #3366FF","youtube: 274.830380<br />sales: 21.503625<br />facebook: #3366FF","youtube: 279.322025<br />sales: 21.717143<br />facebook: #3366FF","youtube: 283.813671<br />sales: 21.930661<br />facebook: #3366FF","youtube: 288.305316<br />sales: 22.144178<br />facebook: #3366FF","youtube: 292.796962<br />sales: 22.357696<br />facebook: #3366FF","youtube: 297.288608<br />sales: 22.571214<br />facebook: #3366FF","youtube: 301.780253<br />sales: 22.784732<br />facebook: #3366FF","youtube: 306.271899<br />sales: 22.998249<br />facebook: #3366FF","youtube: 310.763544<br />sales: 23.211767<br />facebook: #3366FF","youtube: 315.255190<br />sales: 23.425285<br />facebook: #3366FF","youtube: 319.746835<br />sales: 23.638803<br />facebook: #3366FF","youtube: 324.238481<br />sales: 23.852320<br />facebook: #3366FF","youtube: 328.730127<br />sales: 24.065838<br />facebook: #3366FF","youtube: 333.221772<br />sales: 24.279356<br />facebook: #3366FF","youtube: 337.713418<br />sales: 24.492874<br />facebook: #3366FF","youtube: 342.205063<br />sales: 24.706391<br />facebook: #3366FF","youtube: 346.696709<br />sales: 24.919909<br />facebook: #3366FF","youtube: 351.188354<br />sales: 25.133427<br />facebook: #3366FF","youtube: 355.680000<br />sales: 25.346945<br />facebook: #3366FF"],"type":"scatter","mode":"lines","name":"fitted values","line":{"width":3.77952755905512,"color":"rgba(51,102,255,1)","dash":"solid"},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[0],"y":[10],"name":"99_426a7f45792e58d5d7ffa141cbc0216e","type":"scatter","mode":"markers","opacity":0,"hoverinfo":"skip","showlegend":false,"marker":{"color":[0,1],"colorscale":[[0,"#132B43"],[0.00334448160535117,"#132B44"],[0.00668896321070234,"#132C44"],[0.0100334448160535,"#142C45"],[0.0133779264214047,"#142D45"],[0.0167224080267559,"#142D46"],[0.020066889632107,"#142D46"],[0.0234113712374582,"#142E47"],[0.0267558528428094,"#152E47"],[0.0301003344481605,"#152F48"],[0.0334448160535117,"#152F48"],[0.0367892976588629,"#152F49"],[0.040133779264214,"#153049"],[0.0434782608695652,"#16304A"],[0.0468227424749164,"#16304A"],[0.0501672240802676,"#16314B"],[0.0535117056856187,"#16314B"],[0.0568561872909699,"#16324C"],[0.0602006688963211,"#17324D"],[0.0635451505016722,"#17324D"],[0.0668896321070234,"#17334E"],[0.0702341137123746,"#17334E"],[0.0735785953177257,"#17344F"],[0.0769230769230769,"#18344F"],[0.0802675585284281,"#183450"],[0.0836120401337793,"#183550"],[0.0869565217391304,"#183551"],[0.0903010033444816,"#183651"],[0.0936454849498328,"#193652"],[0.0969899665551839,"#193652"],[0.100334448160535,"#193753"],[0.103678929765886,"#193754"],[0.107023411371237,"#193854"],[0.110367892976589,"#1A3855"],[0.11371237458194,"#1A3955"],[0.117056856187291,"#1A3956"],[0.120401337792642,"#1A3956"],[0.123745819397993,"#1A3A57"],[0.127090301003344,"#1B3A57"],[0.130434782608696,"#1B3B58"],[0.133779264214047,"#1B3B59"],[0.137123745819398,"#1B3B59"],[0.140468227424749,"#1C3C5A"],[0.1438127090301,"#1C3C5A"],[0.147157190635451,"#1C3D5B"],[0.150501672240803,"#1C3D5B"],[0.153846153846154,"#1C3D5C"],[0.157190635451505,"#1D3E5C"],[0.160535117056856,"#1D3E5D"],[0.163879598662207,"#1D3F5D"],[0.167224080267559,"#1D3F5E"],[0.17056856187291,"#1D3F5F"],[0.173913043478261,"#1E405F"],[0.177257525083612,"#1E4060"],[0.180602006688963,"#1E4160"],[0.183946488294314,"#1E4161"],[0.187290969899666,"#1E4261"],[0.190635451505017,"#1F4262"],[0.193979933110368,"#1F4263"],[0.197324414715719,"#1F4363"],[0.20066889632107,"#1F4364"],[0.204013377926421,"#1F4464"],[0.207357859531773,"#204465"],[0.210702341137124,"#204465"],[0.214046822742475,"#204566"],[0.217391304347826,"#204566"],[0.220735785953177,"#214667"],[0.224080267558528,"#214668"],[0.22742474916388,"#214768"],[0.230769230769231,"#214769"],[0.234113712374582,"#214769"],[0.237458193979933,"#22486A"],[0.240802675585284,"#22486A"],[0.244147157190635,"#22496B"],[0.247491638795987,"#22496C"],[0.250836120401338,"#224A6C"],[0.254180602006689,"#234A6D"],[0.25752508361204,"#234A6D"],[0.260869565217391,"#234B6E"],[0.264214046822742,"#234B6E"],[0.267558528428094,"#244C6F"],[0.270903010033445,"#244C70"],[0.274247491638796,"#244C70"],[0.277591973244147,"#244D71"],[0.280936454849498,"#244D71"],[0.284280936454849,"#254E72"],[0.287625418060201,"#254E72"],[0.290969899665552,"#254F73"],[0.294314381270903,"#254F74"],[0.297658862876254,"#254F74"],[0.301003344481605,"#265075"],[0.304347826086956,"#265075"],[0.307692307692308,"#265176"],[0.311036789297659,"#265176"],[0.31438127090301,"#275277"],[0.317725752508361,"#275278"],[0.321070234113712,"#275278"],[0.324414715719064,"#275379"],[0.327759197324415,"#275379"],[0.331103678929766,"#28547A"],[0.334448160535117,"#28547B"],[0.337792642140468,"#28557B"],[0.341137123745819,"#28557C"],[0.344481605351171,"#28567C"],[0.347826086956522,"#29567D"],[0.351170568561873,"#29567D"],[0.354515050167224,"#29577E"],[0.357859531772575,"#29577F"],[0.361204013377926,"#2A587F"],[0.364548494983278,"#2A5880"],[0.367892976588629,"#2A5980"],[0.37123745819398,"#2A5981"],[0.374581939799331,"#2A5982"],[0.377926421404682,"#2B5A82"],[0.381270903010033,"#2B5A83"],[0.384615384615385,"#2B5B83"],[0.387959866220736,"#2B5B84"],[0.391304347826087,"#2C5C85"],[0.394648829431438,"#2C5C85"],[0.397993311036789,"#2C5D86"],[0.40133779264214,"#2C5D86"],[0.404682274247492,"#2C5D87"],[0.408026755852843,"#2D5E87"],[0.411371237458194,"#2D5E88"],[0.414715719063545,"#2D5F89"],[0.418060200668896,"#2D5F89"],[0.421404682274247,"#2E608A"],[0.424749163879599,"#2E608A"],[0.42809364548495,"#2E618B"],[0.431438127090301,"#2E618C"],[0.434782608695652,"#2E618C"],[0.438127090301003,"#2F628D"],[0.441471571906354,"#2F628D"],[0.444816053511706,"#2F638E"],[0.448160535117057,"#2F638F"],[0.451505016722408,"#30648F"],[0.454849498327759,"#306490"],[0.45819397993311,"#306590"],[0.461538461538462,"#306591"],[0.464882943143813,"#306592"],[0.468227424749164,"#316692"],[0.471571906354515,"#316693"],[0.474916387959866,"#316793"],[0.478260869565217,"#316794"],[0.481605351170569,"#326895"],[0.48494983277592,"#326895"],[0.488294314381271,"#326996"],[0.491638795986622,"#326996"],[0.494983277591973,"#326997"],[0.498327759197324,"#336A98"],[0.501672240802676,"#336A98"],[0.505016722408027,"#336B99"],[0.508361204013378,"#336B99"],[0.511705685618729,"#346C9A"],[0.51505016722408,"#346C9B"],[0.518394648829431,"#346D9B"],[0.521739130434783,"#346D9C"],[0.525083612040134,"#346E9D"],[0.528428093645485,"#356E9D"],[0.531772575250836,"#356E9E"],[0.535117056856187,"#356F9E"],[0.538461538461538,"#356F9F"],[0.54180602006689,"#3670A0"],[0.545150501672241,"#3670A0"],[0.548494983277592,"#3671A1"],[0.551839464882943,"#3671A1"],[0.555183946488294,"#3772A2"],[0.558528428093645,"#3772A3"],[0.561872909698997,"#3773A3"],[0.565217391304348,"#3773A4"],[0.568561872909699,"#3773A4"],[0.57190635451505,"#3874A5"],[0.575250836120401,"#3874A6"],[0.578595317725752,"#3875A6"],[0.581939799331104,"#3875A7"],[0.585284280936455,"#3976A8"],[0.588628762541806,"#3976A8"],[0.591973244147157,"#3977A9"],[0.595317725752508,"#3977A9"],[0.598662207357859,"#3978AA"],[0.602006688963211,"#3A78AB"],[0.605351170568562,"#3A79AB"],[0.608695652173913,"#3A79AC"],[0.612040133779264,"#3A79AC"],[0.615384615384615,"#3B7AAD"],[0.618729096989967,"#3B7AAE"],[0.622073578595318,"#3B7BAE"],[0.625418060200669,"#3B7BAF"],[0.62876254180602,"#3C7CB0"],[0.632107023411371,"#3C7CB0"],[0.635451505016722,"#3C7DB1"],[0.638795986622074,"#3C7DB1"],[0.642140468227425,"#3C7EB2"],[0.645484949832776,"#3D7EB3"],[0.648829431438127,"#3D7FB3"],[0.652173913043478,"#3D7FB4"],[0.655518394648829,"#3D7FB5"],[0.658862876254181,"#3E80B5"],[0.662207357859532,"#3E80B6"],[0.665551839464883,"#3E81B6"],[0.668896321070234,"#3E81B7"],[0.672240802675585,"#3F82B8"],[0.675585284280936,"#3F82B8"],[0.678929765886288,"#3F83B9"],[0.682274247491639,"#3F83BA"],[0.68561872909699,"#4084BA"],[0.688963210702341,"#4084BB"],[0.692307692307692,"#4085BB"],[0.695652173913043,"#4085BC"],[0.698996655518395,"#4086BD"],[0.702341137123746,"#4186BD"],[0.705685618729097,"#4186BE"],[0.709030100334448,"#4187BF"],[0.712374581939799,"#4187BF"],[0.71571906354515,"#4288C0"],[0.719063545150502,"#4288C1"],[0.722408026755853,"#4289C1"],[0.725752508361204,"#4289C2"],[0.729096989966555,"#438AC2"],[0.732441471571906,"#438AC3"],[0.735785953177257,"#438BC4"],[0.739130434782609,"#438BC4"],[0.74247491638796,"#438CC5"],[0.745819397993311,"#448CC6"],[0.749163879598662,"#448DC6"],[0.752508361204013,"#448DC7"],[0.755852842809364,"#448EC8"],[0.759197324414716,"#458EC8"],[0.762541806020067,"#458FC9"],[0.765886287625418,"#458FC9"],[0.769230769230769,"#458FCA"],[0.77257525083612,"#4690CB"],[0.775919732441471,"#4690CB"],[0.779264214046823,"#4691CC"],[0.782608695652174,"#4691CD"],[0.785953177257525,"#4792CD"],[0.789297658862876,"#4792CE"],[0.792642140468227,"#4793CF"],[0.795986622073579,"#4793CF"],[0.79933110367893,"#4894D0"],[0.802675585284281,"#4894D0"],[0.806020066889632,"#4895D1"],[0.809364548494983,"#4895D2"],[0.812709030100334,"#4896D2"],[0.816053511705686,"#4996D3"],[0.819397993311037,"#4997D4"],[0.822742474916388,"#4997D4"],[0.826086956521739,"#4998D5"],[0.82943143812709,"#4A98D6"],[0.832775919732441,"#4A99D6"],[0.836120401337793,"#4A99D7"],[0.839464882943144,"#4A9AD8"],[0.842809364548495,"#4B9AD8"],[0.846153846153846,"#4B9BD9"],[0.849498327759197,"#4B9BDA"],[0.852842809364548,"#4B9BDA"],[0.8561872909699,"#4C9CDB"],[0.859531772575251,"#4C9CDB"],[0.862876254180602,"#4C9DDC"],[0.866220735785953,"#4C9DDD"],[0.869565217391304,"#4D9EDD"],[0.872909698996655,"#4D9EDE"],[0.876254180602007,"#4D9FDF"],[0.879598662207358,"#4D9FDF"],[0.882943143812709,"#4DA0E0"],[0.88628762541806,"#4EA0E1"],[0.889632107023411,"#4EA1E1"],[0.892976588628762,"#4EA1E2"],[0.896321070234114,"#4EA2E3"],[0.899665551839465,"#4FA2E3"],[0.903010033444816,"#4FA3E4"],[0.906354515050167,"#4FA3E5"],[0.909698996655518,"#4FA4E5"],[0.91304347826087,"#50A4E6"],[0.916387959866221,"#50A5E7"],[0.919732441471572,"#50A5E7"],[0.923076923076923,"#50A6E8"],[0.926421404682274,"#51A6E8"],[0.929765886287625,"#51A7E9"],[0.933110367892977,"#51A7EA"],[0.936454849498328,"#51A8EA"],[0.939799331103679,"#52A8EB"],[0.94314381270903,"#52A9EC"],[0.946488294314381,"#52A9EC"],[0.949832775919732,"#52AAED"],[0.953177257525084,"#53AAEE"],[0.956521739130435,"#53ABEE"],[0.959866220735786,"#53ABEF"],[0.963210702341137,"#53ACF0"],[0.966555183946488,"#54ACF0"],[0.969899665551839,"#54ADF1"],[0.973244147157191,"#54ADF2"],[0.976588628762542,"#54AEF2"],[0.979933110367893,"#55AEF3"],[0.983277591973244,"#55AFF4"],[0.986622073578595,"#55AFF4"],[0.989966555183946,"#55B0F5"],[0.993311036789298,"#56B0F6"],[0.996655518394649,"#56B1F6"],[1,"#56B1F7"]],"colorbar":{"bgcolor":null,"bordercolor":null,"borderwidth":0,"thickness":23.04,"title":"facebook","titlefont":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187},"tickmode":"array","ticktext":["0","10","20","30","40","50"],"tickvals":[0,0.168010752688172,0.336021505376344,0.504032258064516,0.672043010752688,0.84005376344086],"tickfont":{"color":"rgba(0,0,0,1)","family":"","size":11.689497716895},"ticklen":2,"len":0.5}},"xaxis":"x","yaxis":"y","frame":null}],"layout":{"margin":{"t":28.1765601217656,"r":7.30593607305936,"b":42.130898021309,"l":37.2602739726027},"font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187},"xaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[-16.902,373.422],"tickmode":"array","ticktext":["0","100","200","300"],"tickvals":[0,100,200,300],"categoryorder":"array","categoryarray":["0","100","200","300"],"nticks":null,"ticks":"","tickcolor":null,"ticklen":3.65296803652968,"tickwidth":0,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.689497716895},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176,"zeroline":false,"anchor":"y","title":{"text":"youtube","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"yaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[0.396,33.924],"tickmode":"array","ticktext":["10","20","30"],"tickvals":[10,20,30],"categoryorder":"array","categoryarray":["10","20","30"],"nticks":null,"ticks":"","tickcolor":null,"ticklen":3.65296803652968,"tickwidth":0,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.689497716895},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176,"zeroline":false,"anchor":"x","title":{"text":"sales","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"shapes":[{"type":"rect","fillcolor":null,"line":{"color":null,"width":0,"linetype":[]},"yref":"paper","xref":"paper","x0":0,"x1":1,"y0":0,"y1":1}],"showlegend":false,"legend":{"bgcolor":null,"bordercolor":null,"borderwidth":0,"font":{"color":"rgba(0,0,0,1)","family":"","size":11.689497716895}},"hovermode":"closest","barmode":"relative"},"config":{"doubleClick":"reset","showSendToCloud":false},"source":"A","attrs":{"1ecf7ea30cc7":{"x":{},"y":{},"colour":{},"type":"scatter"},"1ecf29c1dc5":{"x":{},"y":{},"colour":{}}},"cur_data":"1ecf7ea30cc7","visdat":{"1ecf7ea30cc7":["function (y) ","x"],"1ecf29c1dc5":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.2,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- ## Fit one more additive model Fit another additive regression model using `sales` as dependent variable, and `youtube`, `facebook`, and `newspaper` as predictors. -- ```r mod_add2 <- lm(sales ~ youtube + facebook + newspaper, data = dat3) summary(mod_add2) ``` ``` ## ## Call: ## lm(formula = sales ~ youtube + facebook + newspaper, data = dat3) ## ## Residuals: ## Min 1Q Median 3Q Max ## -10.5932 -1.0690 0.2902 1.4272 3.3951 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 3.526667 0.374290 9.422 <2e-16 *** ## youtube 0.045765 0.001395 32.809 <2e-16 *** ## facebook 0.188530 0.008611 21.893 <2e-16 *** ## newspaper -0.001037 0.005871 -0.177 0.86 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 2.023 on 196 degrees of freedom ## Multiple R-squared: 0.8972, Adjusted R-squared: 0.8956 ## F-statistic: 570.3 on 3 and 196 DF, p-value: < 2.2e-16 ``` --- ## Summary: additive model ```r summary(mod_add2)$coefficients ``` ``` ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 3.526667243 0.374289884 9.4222884 1.267295e-17 ## youtube 0.045764645 0.001394897 32.8086244 1.509960e-81 ## facebook 0.188530017 0.008611234 21.8934961 1.505339e-54 ## newspaper -0.001037493 0.005871010 -0.1767146 8.599151e-01 ``` -- `$$\text{sales} = 3.527 + 0.046 \cdot \text{youtube} + 0.189 \cdot \text{facebook} - 0.001 \cdot \text{newspaper} + \varepsilon$$` --- ## Fit an interactive model Fit an interactive regression model using `sales` as dependent variable, and `youtube` and `facebook` as predictors. ``` ## ## Call: ## lm(formula = sales ~ youtube * facebook, data = dat3) ## ## Residuals: ## Min 1Q Median 3Q Max ## -7.6039 -0.4833 0.2197 0.7137 1.8295 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 8.100e+00 2.974e-01 27.233 <2e-16 *** ## youtube 1.910e-02 1.504e-03 12.699 <2e-16 *** ## facebook 2.886e-02 8.905e-03 3.241 0.0014 ** ## youtube:facebook 9.054e-04 4.368e-05 20.727 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 1.132 on 196 degrees of freedom ## Multiple R-squared: 0.9678, Adjusted R-squared: 0.9673 ## F-statistic: 1963 on 3 and 196 DF, p-value: < 2.2e-16 ``` --- ## Summary: interactive model ``` ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 8.1002642437 2.974456e-01 27.232755 1.541461e-68 ## youtube 0.0191010738 1.504146e-03 12.698953 2.363605e-27 ## facebook 0.0288603399 8.905273e-03 3.240815 1.400461e-03 ## youtube:facebook 0.0009054122 4.368366e-05 20.726564 2.757681e-51 ``` `$$\text{sales} = 8.100 + 0.019 \cdot \text{youtube} + 0.289 \cdot \text{facebook} + 0.001 \cdot \text{youtube} \times \text{facebook}$$` --- ## Visualize: interactive model ```r p <- ggplot(dat3, aes(x = youtube, y = sales, color = facebook)) + geom_point() + geom_smooth(method = "lm", se = FALSE, data = dat3[dat3$facebook > 25, ]) + geom_smooth(method = "lm", se = FALSE, data = dat3[dat3$facebook <= 25, ]) + theme_minimal() ggplotly(p) ``` <div id="htmlwidget-6164c9f0fbb3720cf9b1" style="width:720px;height:432px;" class="plotly html-widget"></div> <script type="application/json" data-for="htmlwidget-6164c9f0fbb3720cf9b1">{"x":{"data":[{"x":[276.12,53.4,20.64,181.8,216.96,10.44,69,144.24,10.32,239.76,79.32,257.64,28.56,117,244.92,234.48,81.36,337.68,83.04,176.76,262.08,284.88,15.84,273.96,74.76,315.48,171.48,288.12,298.56,84.72,351.48,135.48,116.64,318.72,114.84,348.84,320.28,89.64,51.72,273.6,243,212.4,352.32,248.28,30.12,210.12,107.64,287.88,272.64,80.28,239.76,120.48,259.68,219.12,315.24,238.68,8.76,163.44,252.96,252.84,64.2,313.56,287.16,123.24,157.32,82.8,37.8,167.16,284.88,260.16,238.92,131.76,32.16,155.28,256.08,20.28,33,144.6,6.48,139.2,91.68,287.76,90.36,82.08,256.2,231.84,91.56,132.84,105.96,131.76,161.16,34.32,261.24,301.08,128.88,195.96,237.12,221.88,347.64,162.24,266.88,355.68,336.24,225.48,285.84,165.48,30,108.48,15.72,306.48,270.96,290.04,210.84,251.52,93.84,90.12,167.04,91.68,150.84,23.28,169.56,22.56,268.8,147.72,275.4,104.64,9.36,96.24,264.36,71.52,0.84,318.24,10.08,263.76,44.28,57.96,30.72,328.44,51.6,221.88,88.08,232.44,264.6,125.52,115.44,168.36,288.12,291.84,45.6,53.64,336.84,145.2,237.12,205.56,225.36,4.92,112.68,179.76,14.04,158.04,207,102.84,226.08,196.2,140.64,281.4,21.48,248.16,258.48,341.16,60,197.4,23.52,202.08,266.88,332.28,298.08,204.24,332.04,198.72,187.92,262.2,67.44,345.12,304.56,246,167.4,229.32,343.2,22.44,47.4,90.6,20.64,200.16,179.64,45.84,113.04,212.4,340.32,278.52],"y":[26.52,12.48,11.16,22.2,15.48,8.64,14.16,15.84,5.76,12.72,10.32,20.88,11.04,11.64,22.8,26.88,15,29.28,13.56,17.52,21.6,15,6.72,18.6,11.64,14.4,18,19.08,22.68,12.6,25.68,14.28,11.52,20.88,11.4,15.36,30.48,17.64,12.12,25.8,19.92,20.52,24.84,15.48,10.2,17.88,12.72,27.84,17.76,11.64,13.68,12.84,27.12,25.44,24.24,28.44,6.6,15.84,28.56,22.08,9.72,29.04,18.84,16.8,21.6,11.16,11.4,16.08,22.68,26.76,21.96,14.88,10.56,13.2,20.4,10.44,8.28,17.04,6.36,13.2,14.16,14.76,13.56,16.32,26.04,18.24,14.4,19.2,15.48,20.04,13.44,8.76,23.28,26.64,13.8,20.28,14.04,18.6,30.48,20.64,14.04,28.56,17.76,17.64,24.84,23.04,8.64,10.44,6.36,23.76,16.08,26.16,16.92,19.08,17.52,15.12,14.64,11.28,19.08,7.92,18.6,8.4,13.92,18.24,23.64,12.72,7.92,10.56,29.64,11.64,1.92,15.24,6.84,23.52,12.96,13.92,11.4,24.96,11.52,24.84,13.08,23.04,24.12,12.48,13.68,12.36,15.84,30.48,13.08,12.12,19.32,13.92,19.92,22.8,18.72,3.84,18.36,12.12,8.76,15.48,17.28,15.96,17.88,21.6,14.28,14.28,9.6,14.64,20.52,18,10.08,17.4,9.12,14.04,13.8,32.4,24.24,14.04,14.16,15.12,12.6,14.64,10.44,31.44,21.12,27.12,12.36,20.76,19.08,8.04,12.96,11.88,7.08,23.52,20.76,9.12,11.64,15.36,30.6,16.08],"text":["youtube: 276.12<br />sales: 26.52<br />facebook: 45.36","youtube: 53.40<br />sales: 12.48<br />facebook: 47.16","youtube: 20.64<br />sales: 11.16<br />facebook: 55.08","youtube: 181.80<br />sales: 22.20<br />facebook: 49.56","youtube: 216.96<br />sales: 15.48<br />facebook: 12.96","youtube: 10.44<br />sales: 8.64<br />facebook: 58.68","youtube: 69.00<br />sales: 14.16<br />facebook: 39.36","youtube: 144.24<br />sales: 15.84<br />facebook: 23.52","youtube: 10.32<br />sales: 5.76<br />facebook: 2.52","youtube: 239.76<br />sales: 12.72<br />facebook: 3.12","youtube: 79.32<br />sales: 10.32<br />facebook: 6.96","youtube: 257.64<br />sales: 20.88<br />facebook: 28.80","youtube: 28.56<br />sales: 11.04<br />facebook: 42.12","youtube: 117.00<br />sales: 11.64<br />facebook: 9.12","youtube: 244.92<br />sales: 22.80<br />facebook: 39.48","youtube: 234.48<br />sales: 26.88<br />facebook: 57.24","youtube: 81.36<br />sales: 15.00<br />facebook: 43.92","youtube: 337.68<br />sales: 29.28<br />facebook: 47.52","youtube: 83.04<br />sales: 13.56<br />facebook: 24.60","youtube: 176.76<br />sales: 17.52<br />facebook: 28.68","youtube: 262.08<br />sales: 21.60<br />facebook: 33.24","youtube: 284.88<br />sales: 15.00<br />facebook: 6.12","youtube: 15.84<br />sales: 6.72<br />facebook: 19.08","youtube: 273.96<br />sales: 18.60<br />facebook: 20.28","youtube: 74.76<br />sales: 11.64<br />facebook: 15.12","youtube: 315.48<br />sales: 14.40<br />facebook: 4.20","youtube: 171.48<br />sales: 18.00<br />facebook: 35.16","youtube: 288.12<br />sales: 19.08<br />facebook: 20.04","youtube: 298.56<br />sales: 22.68<br />facebook: 32.52","youtube: 84.72<br />sales: 12.60<br />facebook: 19.20","youtube: 351.48<br />sales: 25.68<br />facebook: 33.96","youtube: 135.48<br />sales: 14.28<br />facebook: 20.88","youtube: 116.64<br />sales: 11.52<br />facebook: 1.80","youtube: 318.72<br />sales: 20.88<br />facebook: 24.00","youtube: 114.84<br />sales: 11.40<br />facebook: 1.68","youtube: 348.84<br />sales: 15.36<br />facebook: 4.92","youtube: 320.28<br />sales: 30.48<br />facebook: 52.56","youtube: 89.64<br />sales: 17.64<br />facebook: 59.28","youtube: 51.72<br />sales: 12.12<br />facebook: 32.04","youtube: 273.60<br />sales: 25.80<br />facebook: 45.24","youtube: 243.00<br />sales: 19.92<br />facebook: 26.76","youtube: 212.40<br />sales: 20.52<br />facebook: 40.08","youtube: 352.32<br />sales: 24.84<br />facebook: 33.24","youtube: 248.28<br />sales: 15.48<br />facebook: 10.08","youtube: 30.12<br />sales: 10.20<br />facebook: 30.84","youtube: 210.12<br />sales: 17.88<br />facebook: 27.00","youtube: 107.64<br />sales: 12.72<br />facebook: 11.88","youtube: 287.88<br />sales: 27.84<br />facebook: 49.80","youtube: 272.64<br />sales: 17.76<br />facebook: 18.96","youtube: 80.28<br />sales: 11.64<br />facebook: 14.04","youtube: 239.76<br />sales: 13.68<br />facebook: 3.72","youtube: 120.48<br />sales: 12.84<br />facebook: 11.52","youtube: 259.68<br />sales: 27.12<br />facebook: 50.04","youtube: 219.12<br />sales: 25.44<br />facebook: 55.44","youtube: 315.24<br />sales: 24.24<br />facebook: 34.56","youtube: 238.68<br />sales: 28.44<br />facebook: 59.28","youtube: 8.76<br />sales: 6.60<br />facebook: 33.72","youtube: 163.44<br />sales: 15.84<br />facebook: 23.04","youtube: 252.96<br />sales: 28.56<br />facebook: 59.52","youtube: 252.84<br />sales: 22.08<br />facebook: 35.40","youtube: 64.20<br />sales: 9.72<br />facebook: 2.40","youtube: 313.56<br />sales: 29.04<br />facebook: 51.24","youtube: 287.16<br />sales: 18.84<br />facebook: 18.60","youtube: 123.24<br />sales: 16.80<br />facebook: 35.52","youtube: 157.32<br />sales: 21.60<br />facebook: 51.36","youtube: 82.80<br />sales: 11.16<br />facebook: 11.16","youtube: 37.80<br />sales: 11.40<br />facebook: 29.52","youtube: 167.16<br />sales: 16.08<br />facebook: 17.40","youtube: 284.88<br />sales: 22.68<br />facebook: 33.00","youtube: 260.16<br />sales: 26.76<br />facebook: 52.68","youtube: 238.92<br />sales: 21.96<br />facebook: 36.72","youtube: 131.76<br />sales: 14.88<br />facebook: 17.16","youtube: 32.16<br />sales: 10.56<br />facebook: 39.60","youtube: 155.28<br />sales: 13.20<br />facebook: 6.84","youtube: 256.08<br />sales: 20.40<br />facebook: 29.52","youtube: 20.28<br />sales: 10.44<br />facebook: 52.44","youtube: 33.00<br />sales: 8.28<br />facebook: 1.92","youtube: 144.60<br />sales: 17.04<br />facebook: 34.20","youtube: 6.48<br />sales: 6.36<br />facebook: 35.88","youtube: 139.20<br />sales: 13.20<br />facebook: 9.24","youtube: 91.68<br />sales: 14.16<br />facebook: 32.04","youtube: 287.76<br />sales: 14.76<br />facebook: 4.92","youtube: 90.36<br />sales: 13.56<br />facebook: 24.36","youtube: 82.08<br />sales: 16.32<br />facebook: 53.40","youtube: 256.20<br />sales: 26.04<br />facebook: 51.60","youtube: 231.84<br />sales: 18.24<br />facebook: 22.08","youtube: 91.56<br />sales: 14.40<br />facebook: 33.00","youtube: 132.84<br />sales: 19.20<br />facebook: 48.72","youtube: 105.96<br />sales: 15.48<br />facebook: 30.60","youtube: 131.76<br />sales: 20.04<br />facebook: 57.36","youtube: 161.16<br />sales: 13.44<br />facebook: 5.88","youtube: 34.32<br />sales: 8.76<br />facebook: 1.80","youtube: 261.24<br />sales: 23.28<br />facebook: 40.20","youtube: 301.08<br />sales: 26.64<br />facebook: 43.80","youtube: 128.88<br />sales: 13.80<br />facebook: 16.80","youtube: 195.96<br />sales: 20.28<br />facebook: 37.92","youtube: 237.12<br />sales: 14.04<br />facebook: 4.20","youtube: 221.88<br />sales: 18.60<br />facebook: 25.20","youtube: 347.64<br />sales: 30.48<br />facebook: 50.76","youtube: 162.24<br />sales: 20.64<br />facebook: 50.04","youtube: 266.88<br />sales: 14.04<br />facebook: 5.16","youtube: 355.68<br />sales: 28.56<br />facebook: 43.56","youtube: 336.24<br />sales: 17.76<br />facebook: 12.12","youtube: 225.48<br />sales: 17.64<br />facebook: 20.64","youtube: 285.84<br />sales: 24.84<br />facebook: 41.16","youtube: 165.48<br />sales: 23.04<br />facebook: 55.68","youtube: 30.00<br />sales: 8.64<br />facebook: 13.20","youtube: 108.48<br />sales: 10.44<br />facebook: 0.36","youtube: 15.72<br />sales: 6.36<br />facebook: 0.48","youtube: 306.48<br />sales: 23.76<br />facebook: 32.28","youtube: 270.96<br />sales: 16.08<br />facebook: 9.84","youtube: 290.04<br />sales: 26.16<br />facebook: 45.60","youtube: 210.84<br />sales: 16.92<br />facebook: 18.48","youtube: 251.52<br />sales: 19.08<br />facebook: 24.72","youtube: 93.84<br />sales: 17.52<br />facebook: 56.16","youtube: 90.12<br />sales: 15.12<br />facebook: 42.00","youtube: 167.04<br />sales: 14.64<br />facebook: 17.16","youtube: 91.68<br />sales: 11.28<br />facebook: 0.96","youtube: 150.84<br />sales: 19.08<br />facebook: 44.28","youtube: 23.28<br />sales: 7.92<br />facebook: 19.20","youtube: 169.56<br />sales: 18.60<br />facebook: 32.16","youtube: 22.56<br />sales: 8.40<br />facebook: 26.04","youtube: 268.80<br />sales: 13.92<br />facebook: 2.88","youtube: 147.72<br />sales: 18.24<br />facebook: 41.52","youtube: 275.40<br />sales: 23.64<br />facebook: 38.76","youtube: 104.64<br />sales: 12.72<br />facebook: 14.16","youtube: 9.36<br />sales: 7.92<br />facebook: 46.68","youtube: 96.24<br />sales: 10.56<br />facebook: 0.00","youtube: 264.36<br />sales: 29.64<br />facebook: 58.80","youtube: 71.52<br />sales: 11.64<br />facebook: 14.40","youtube: 0.84<br />sales: 1.92<br />facebook: 47.52","youtube: 318.24<br />sales: 15.24<br />facebook: 3.48","youtube: 10.08<br />sales: 6.84<br />facebook: 32.64","youtube: 263.76<br />sales: 23.52<br />facebook: 40.20","youtube: 44.28<br />sales: 12.96<br />facebook: 46.32","youtube: 57.96<br />sales: 13.92<br />facebook: 56.40","youtube: 30.72<br />sales: 11.40<br />facebook: 46.80","youtube: 328.44<br />sales: 24.96<br />facebook: 34.68","youtube: 51.60<br />sales: 11.52<br />facebook: 31.08","youtube: 221.88<br />sales: 24.84<br />facebook: 52.68","youtube: 88.08<br />sales: 13.08<br />facebook: 20.40","youtube: 232.44<br />sales: 23.04<br />facebook: 42.48","youtube: 264.60<br />sales: 24.12<br />facebook: 39.84","youtube: 125.52<br />sales: 12.48<br />facebook: 6.84","youtube: 115.44<br />sales: 13.68<br />facebook: 17.76","youtube: 168.36<br />sales: 12.36<br />facebook: 2.28","youtube: 288.12<br />sales: 15.84<br />facebook: 8.76","youtube: 291.84<br />sales: 30.48<br />facebook: 58.80","youtube: 45.60<br />sales: 13.08<br />facebook: 48.36","youtube: 53.64<br />sales: 12.12<br />facebook: 30.96","youtube: 336.84<br />sales: 19.32<br />facebook: 16.68","youtube: 145.20<br />sales: 13.92<br />facebook: 10.08","youtube: 237.12<br />sales: 19.92<br />facebook: 27.96","youtube: 205.56<br />sales: 22.80<br />facebook: 47.64","youtube: 225.36<br />sales: 18.72<br />facebook: 25.32","youtube: 4.92<br />sales: 3.84<br />facebook: 13.92","youtube: 112.68<br />sales: 18.36<br />facebook: 52.20","youtube: 179.76<br />sales: 12.12<br />facebook: 1.56","youtube: 14.04<br />sales: 8.76<br />facebook: 44.28","youtube: 158.04<br />sales: 15.48<br />facebook: 22.08","youtube: 207.00<br />sales: 17.28<br />facebook: 21.72","youtube: 102.84<br />sales: 15.96<br />facebook: 42.96","youtube: 226.08<br />sales: 17.88<br />facebook: 21.72","youtube: 196.20<br />sales: 21.60<br />facebook: 44.16","youtube: 140.64<br />sales: 14.28<br />facebook: 17.64","youtube: 281.40<br />sales: 14.28<br />facebook: 4.08","youtube: 21.48<br />sales: 9.60<br />facebook: 45.12","youtube: 248.16<br />sales: 14.64<br />facebook: 6.24","youtube: 258.48<br />sales: 20.52<br />facebook: 28.32","youtube: 341.16<br />sales: 18.00<br />facebook: 12.72","youtube: 60.00<br />sales: 10.08<br />facebook: 13.92","youtube: 197.40<br />sales: 17.40<br />facebook: 25.08","youtube: 23.52<br />sales: 9.12<br />facebook: 24.12","youtube: 202.08<br />sales: 14.04<br />facebook: 8.52","youtube: 266.88<br />sales: 13.80<br />facebook: 4.08","youtube: 332.28<br />sales: 32.40<br />facebook: 58.68","youtube: 298.08<br />sales: 24.24<br />facebook: 36.24","youtube: 204.24<br />sales: 14.04<br />facebook: 9.36","youtube: 332.04<br />sales: 14.16<br />facebook: 2.76","youtube: 198.72<br />sales: 15.12<br />facebook: 12.00","youtube: 187.92<br />sales: 12.60<br />facebook: 3.12","youtube: 262.20<br />sales: 14.64<br />facebook: 6.48","youtube: 67.44<br />sales: 10.44<br />facebook: 6.84","youtube: 345.12<br />sales: 31.44<br />facebook: 51.60","youtube: 304.56<br />sales: 21.12<br />facebook: 25.56","youtube: 246.00<br />sales: 27.12<br />facebook: 54.12","youtube: 167.40<br />sales: 12.36<br />facebook: 2.52","youtube: 229.32<br />sales: 20.76<br />facebook: 34.44","youtube: 343.20<br />sales: 19.08<br />facebook: 16.68","youtube: 22.44<br />sales: 8.04<br />facebook: 14.52","youtube: 47.40<br />sales: 12.96<br />facebook: 49.32","youtube: 90.60<br />sales: 11.88<br />facebook: 12.96","youtube: 20.64<br />sales: 7.08<br />facebook: 4.92","youtube: 200.16<br />sales: 23.52<br />facebook: 50.40","youtube: 179.64<br />sales: 20.76<br />facebook: 42.72","youtube: 45.84<br />sales: 9.12<br />facebook: 4.44","youtube: 113.04<br />sales: 11.64<br />facebook: 5.88","youtube: 212.40<br />sales: 15.36<br />facebook: 11.16","youtube: 340.32<br />sales: 30.60<br />facebook: 50.40","youtube: 278.52<br />sales: 16.08<br />facebook: 10.32"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":["rgba(69,142,201,1)","rgba(71,147,206,1)","rgba(81,166,232,1)","rgba(74,153,214,1)","rgba(32,69,103,1)","rgba(85,175,244,1)","rgba(62,128,182,1)","rgba(44,92,133,1)","rgba(22,48,74,1)","rgba(22,49,75,1)","rgba(26,57,86,1)","rgba(50,104,149,1)","rgba(65,135,190,1)","rgba(28,61,92,1)","rgba(62,129,182,1)","rgba(83,171,239,1)","rgba(67,139,196,1)","rgba(71,148,208,1)","rgba(45,95,136,1)","rgba(50,104,149,1)","rgba(55,114,163,1)","rgba(25,55,83,1)","rgba(39,82,120,1)","rgba(40,85,124,1)","rgba(35,74,109,1)","rgba(23,51,78,1)","rgba(57,118,169,1)","rgba(40,85,123,1)","rgba(54,112,160,1)","rgba(39,83,120,1)","rgba(56,116,165,1)","rgba(41,86,125,1)","rgba(21,47,72,1)","rgba(44,93,135,1)","rgba(21,46,71,1)","rgba(24,53,80,1)","rgba(78,160,224,1)","rgba(86,176,246,1)","rgba(53,111,159,1)","rgba(69,142,200,1)","rgba(47,99,143,1)","rgba(63,130,184,1)","rgba(55,114,163,1)","rgba(29,63,94,1)","rgba(52,109,155,1)","rgba(48,100,144,1)","rgba(31,67,99,1)","rgba(74,153,215,1)","rgba(39,82,120,1)","rgba(33,72,106,1)","rgba(23,50,77,1)","rgba(31,66,98,1)","rgba(74,154,216,1)","rgba(81,167,233,1)","rgba(56,117,167,1)","rgba(86,176,246,1)","rgba(55,115,164,1)","rgba(43,91,132,1)","rgba(86,177,247,1)","rgba(57,119,169,1)","rgba(21,48,73,1)","rgba(76,157,220,1)","rgba(38,81,119,1)","rgba(57,119,170,1)","rgba(76,157,220,1)","rgba(30,66,97,1)","rgba(51,106,151,1)","rgba(37,79,115,1)","rgba(54,114,162,1)","rgba(78,160,224,1)","rgba(59,122,173,1)","rgba(37,78,115,1)","rgba(62,129,182,1)","rgba(26,57,85,1)","rgba(51,106,151,1)","rgba(77,160,224,1)","rgba(21,47,72,1)","rgba(56,116,166,1)","rgba(58,120,171,1)","rgba(28,62,92,1)","rgba(53,111,159,1)","rgba(24,53,80,1)","rgba(45,94,136,1)","rgba(79,162,227,1)","rgba(76,158,221,1)","rgba(42,89,129,1)","rgba(54,114,162,1)","rgba(73,151,212,1)","rgba(52,108,155,1)","rgba(83,172,240,1)","rgba(25,55,83,1)","rgba(21,47,72,1)","rgba(63,130,184,1)","rgba(67,139,196,1)","rgba(36,78,113,1)","rgba(60,125,177,1)","rgba(23,51,78,1)","rgba(46,96,138,1)","rgba(75,155,218,1)","rgba(74,154,216,1)","rgba(24,53,81,1)","rgba(67,138,195,1)","rgba(31,68,100,1)","rgba(41,86,125,1)","rgba(64,132,187,1)","rgba(81,168,234,1)","rgba(33,70,103,1)","rgba(19,44,68,1)","rgba(19,44,68,1)","rgba(54,112,160,1)","rgba(29,63,94,1)","rgba(69,143,201,1)","rgba(38,81,118,1)","rgba(45,95,137,1)","rgba(82,169,236,1)","rgba(65,134,190,1)","rgba(37,78,115,1)","rgba(20,45,70,1)","rgba(68,140,197,1)","rgba(39,83,120,1)","rgba(54,112,159,1)","rgba(47,98,141,1)","rgba(22,49,75,1)","rgba(64,133,188,1)","rgba(61,127,180,1)","rgba(34,72,106,1)","rgba(70,146,205,1)","rgba(19,43,67,1)","rgba(85,175,245,1)","rgba(34,72,107,1)","rgba(71,148,208,1)","rgba(23,50,76,1)","rgba(54,113,161,1)","rgba(63,130,184,1)","rgba(70,145,204,1)","rgba(82,169,237,1)","rgba(71,146,205,1)","rgba(56,117,167,1)","rgba(52,109,156,1)","rgba(78,160,224,1)","rgba(40,85,124,1)","rgba(65,136,192,1)","rgba(62,129,183,1)","rgba(26,57,85,1)","rgba(37,80,116,1)","rgba(21,47,73,1)","rgba(28,61,91,1)","rgba(85,175,245,1)","rgba(72,150,210,1)","rgba(52,109,156,1)","rgba(36,77,113,1)","rgba(29,63,94,1)","rgba(49,102,146,1)","rgba(72,148,208,1)","rgba(46,96,139,1)","rgba(33,71,105,1)","rgba(77,159,223,1)","rgba(21,46,71,1)","rgba(68,140,197,1)","rgba(42,89,129,1)","rgba(42,88,128,1)","rgba(66,137,193,1)","rgba(42,88,128,1)","rgba(67,140,197,1)","rgba(37,79,116,1)","rgba(23,51,78,1)","rgba(69,142,200,1)","rgba(25,55,84,1)","rgba(49,103,148,1)","rgba(32,69,102,1)","rgba(33,71,105,1)","rgba(46,96,138,1)","rgba(44,93,135,1)","rgba(28,60,90,1)","rgba(23,51,78,1)","rgba(85,175,244,1)","rgba(58,121,172,1)","rgba(29,62,92,1)","rgba(22,48,74,1)","rgba(31,67,100,1)","rgba(22,49,75,1)","rgba(26,56,84,1)","rgba(26,57,85,1)","rgba(76,158,221,1)","rgba(46,97,139,1)","rgba(79,164,229,1)","rgba(22,48,74,1)","rgba(56,117,166,1)","rgba(36,77,113,1)","rgba(34,73,107,1)","rgba(74,152,213,1)","rgba(32,69,103,1)","rgba(24,53,80,1)","rgba(75,155,217,1)","rgba(66,136,192,1)","rgba(23,52,79,1)","rgba(25,55,83,1)","rgba(30,66,97,1)","rgba(75,155,217,1)","rgba(30,64,95,1)"],"opacity":1,"size":5.66929133858268,"symbol":"circle","line":{"width":1.88976377952756,"color":["rgba(69,142,201,1)","rgba(71,147,206,1)","rgba(81,166,232,1)","rgba(74,153,214,1)","rgba(32,69,103,1)","rgba(85,175,244,1)","rgba(62,128,182,1)","rgba(44,92,133,1)","rgba(22,48,74,1)","rgba(22,49,75,1)","rgba(26,57,86,1)","rgba(50,104,149,1)","rgba(65,135,190,1)","rgba(28,61,92,1)","rgba(62,129,182,1)","rgba(83,171,239,1)","rgba(67,139,196,1)","rgba(71,148,208,1)","rgba(45,95,136,1)","rgba(50,104,149,1)","rgba(55,114,163,1)","rgba(25,55,83,1)","rgba(39,82,120,1)","rgba(40,85,124,1)","rgba(35,74,109,1)","rgba(23,51,78,1)","rgba(57,118,169,1)","rgba(40,85,123,1)","rgba(54,112,160,1)","rgba(39,83,120,1)","rgba(56,116,165,1)","rgba(41,86,125,1)","rgba(21,47,72,1)","rgba(44,93,135,1)","rgba(21,46,71,1)","rgba(24,53,80,1)","rgba(78,160,224,1)","rgba(86,176,246,1)","rgba(53,111,159,1)","rgba(69,142,200,1)","rgba(47,99,143,1)","rgba(63,130,184,1)","rgba(55,114,163,1)","rgba(29,63,94,1)","rgba(52,109,155,1)","rgba(48,100,144,1)","rgba(31,67,99,1)","rgba(74,153,215,1)","rgba(39,82,120,1)","rgba(33,72,106,1)","rgba(23,50,77,1)","rgba(31,66,98,1)","rgba(74,154,216,1)","rgba(81,167,233,1)","rgba(56,117,167,1)","rgba(86,176,246,1)","rgba(55,115,164,1)","rgba(43,91,132,1)","rgba(86,177,247,1)","rgba(57,119,169,1)","rgba(21,48,73,1)","rgba(76,157,220,1)","rgba(38,81,119,1)","rgba(57,119,170,1)","rgba(76,157,220,1)","rgba(30,66,97,1)","rgba(51,106,151,1)","rgba(37,79,115,1)","rgba(54,114,162,1)","rgba(78,160,224,1)","rgba(59,122,173,1)","rgba(37,78,115,1)","rgba(62,129,182,1)","rgba(26,57,85,1)","rgba(51,106,151,1)","rgba(77,160,224,1)","rgba(21,47,72,1)","rgba(56,116,166,1)","rgba(58,120,171,1)","rgba(28,62,92,1)","rgba(53,111,159,1)","rgba(24,53,80,1)","rgba(45,94,136,1)","rgba(79,162,227,1)","rgba(76,158,221,1)","rgba(42,89,129,1)","rgba(54,114,162,1)","rgba(73,151,212,1)","rgba(52,108,155,1)","rgba(83,172,240,1)","rgba(25,55,83,1)","rgba(21,47,72,1)","rgba(63,130,184,1)","rgba(67,139,196,1)","rgba(36,78,113,1)","rgba(60,125,177,1)","rgba(23,51,78,1)","rgba(46,96,138,1)","rgba(75,155,218,1)","rgba(74,154,216,1)","rgba(24,53,81,1)","rgba(67,138,195,1)","rgba(31,68,100,1)","rgba(41,86,125,1)","rgba(64,132,187,1)","rgba(81,168,234,1)","rgba(33,70,103,1)","rgba(19,44,68,1)","rgba(19,44,68,1)","rgba(54,112,160,1)","rgba(29,63,94,1)","rgba(69,143,201,1)","rgba(38,81,118,1)","rgba(45,95,137,1)","rgba(82,169,236,1)","rgba(65,134,190,1)","rgba(37,78,115,1)","rgba(20,45,70,1)","rgba(68,140,197,1)","rgba(39,83,120,1)","rgba(54,112,159,1)","rgba(47,98,141,1)","rgba(22,49,75,1)","rgba(64,133,188,1)","rgba(61,127,180,1)","rgba(34,72,106,1)","rgba(70,146,205,1)","rgba(19,43,67,1)","rgba(85,175,245,1)","rgba(34,72,107,1)","rgba(71,148,208,1)","rgba(23,50,76,1)","rgba(54,113,161,1)","rgba(63,130,184,1)","rgba(70,145,204,1)","rgba(82,169,237,1)","rgba(71,146,205,1)","rgba(56,117,167,1)","rgba(52,109,156,1)","rgba(78,160,224,1)","rgba(40,85,124,1)","rgba(65,136,192,1)","rgba(62,129,183,1)","rgba(26,57,85,1)","rgba(37,80,116,1)","rgba(21,47,73,1)","rgba(28,61,91,1)","rgba(85,175,245,1)","rgba(72,150,210,1)","rgba(52,109,156,1)","rgba(36,77,113,1)","rgba(29,63,94,1)","rgba(49,102,146,1)","rgba(72,148,208,1)","rgba(46,96,139,1)","rgba(33,71,105,1)","rgba(77,159,223,1)","rgba(21,46,71,1)","rgba(68,140,197,1)","rgba(42,89,129,1)","rgba(42,88,128,1)","rgba(66,137,193,1)","rgba(42,88,128,1)","rgba(67,140,197,1)","rgba(37,79,116,1)","rgba(23,51,78,1)","rgba(69,142,200,1)","rgba(25,55,84,1)","rgba(49,103,148,1)","rgba(32,69,102,1)","rgba(33,71,105,1)","rgba(46,96,138,1)","rgba(44,93,135,1)","rgba(28,60,90,1)","rgba(23,51,78,1)","rgba(85,175,244,1)","rgba(58,121,172,1)","rgba(29,62,92,1)","rgba(22,48,74,1)","rgba(31,67,100,1)","rgba(22,49,75,1)","rgba(26,56,84,1)","rgba(26,57,85,1)","rgba(76,158,221,1)","rgba(46,97,139,1)","rgba(79,164,229,1)","rgba(22,48,74,1)","rgba(56,117,166,1)","rgba(36,77,113,1)","rgba(34,73,107,1)","rgba(74,152,213,1)","rgba(32,69,103,1)","rgba(24,53,80,1)","rgba(75,155,217,1)","rgba(66,136,192,1)","rgba(23,52,79,1)","rgba(25,55,83,1)","rgba(30,66,97,1)","rgba(75,155,217,1)","rgba(30,64,95,1)"]}},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[0.84,5.33164556962025,9.8232911392405,14.3149367088608,18.806582278481,23.2982278481013,27.7898734177215,32.2815189873418,36.773164556962,41.2648101265823,45.7564556962025,50.2481012658228,54.739746835443,59.2313924050633,63.7230379746835,68.2146835443038,72.706329113924,77.1979746835443,81.6896202531645,86.1812658227848,90.6729113924051,95.1645569620253,99.6562025316456,104.147848101266,108.639493670886,113.131139240506,117.622784810127,122.114430379747,126.606075949367,131.097721518987,135.589367088608,140.081012658228,144.572658227848,149.064303797468,153.555949367089,158.047594936709,162.539240506329,167.030886075949,171.52253164557,176.01417721519,180.50582278481,184.99746835443,189.489113924051,193.980759493671,198.472405063291,202.964050632911,207.455696202532,211.947341772152,216.438987341772,220.930632911392,225.422278481013,229.913924050633,234.405569620253,238.897215189873,243.388860759494,247.880506329114,252.372151898734,256.863797468354,261.355443037975,265.847088607595,270.338734177215,274.830379746835,279.322025316456,283.813670886076,288.305316455696,292.796962025316,297.288607594937,301.780253164557,306.271898734177,310.763544303797,315.255189873418,319.746835443038,324.238481012658,328.730126582278,333.221772151899,337.713417721519,342.205063291139,346.696708860759,351.18835443038,355.68],"y":[9.24194990523306,9.50176961623485,9.76158932723664,10.0214090382384,10.2812287492402,10.541048460242,10.8008681712438,11.0606878822456,11.3205075932474,11.5803273042492,11.8401470152509,12.0999667262527,12.3597864372545,12.6196061482563,12.8794258592581,13.1392455702599,13.3990652812617,13.6588849922635,13.9187047032652,14.178524414267,14.4383441252688,14.6981638362706,14.9579835472724,15.2178032582742,15.477622969276,15.7374426802778,15.9972623912796,16.2570821022813,16.5169018132831,16.7767215242849,17.0365412352867,17.2963609462885,17.5561806572903,17.8160003682921,18.0758200792939,18.3356397902956,18.5954595012974,18.8552792122992,19.115098923301,19.3749186343028,19.6347383453046,19.8945580563064,20.1543777673082,20.41419747831,20.6740171893117,20.9338369003135,21.1936566113153,21.4534763223171,21.7132960333189,21.9731157443207,22.2329354553225,22.4927551663243,22.752574877326,23.0123945883278,23.2722142993296,23.5320340103314,23.7918537213332,24.051673432335,24.3114931433368,24.5713128543386,24.8311325653404,25.0909522763421,25.3507719873439,25.6105916983457,25.8704114093475,26.1302311203493,26.3900508313511,26.6498705423529,26.9096902533547,27.1695099643564,27.4293296753582,27.68914938636,27.9489690973618,28.2087888083636,28.4686085193654,28.7284282303672,28.988247941369,29.2480676523708,29.5078873633725,29.7677070743743],"text":["youtube: 0.840000<br />sales: 9.241950<br />facebook: #3366FF","youtube: 5.331646<br />sales: 9.501770<br />facebook: #3366FF","youtube: 9.823291<br />sales: 9.761589<br />facebook: #3366FF","youtube: 14.314937<br />sales: 10.021409<br />facebook: #3366FF","youtube: 18.806582<br />sales: 10.281229<br />facebook: #3366FF","youtube: 23.298228<br />sales: 10.541048<br />facebook: #3366FF","youtube: 27.789873<br />sales: 10.800868<br />facebook: #3366FF","youtube: 32.281519<br />sales: 11.060688<br />facebook: #3366FF","youtube: 36.773165<br />sales: 11.320508<br />facebook: #3366FF","youtube: 41.264810<br />sales: 11.580327<br />facebook: #3366FF","youtube: 45.756456<br />sales: 11.840147<br />facebook: #3366FF","youtube: 50.248101<br />sales: 12.099967<br />facebook: #3366FF","youtube: 54.739747<br />sales: 12.359786<br />facebook: #3366FF","youtube: 59.231392<br />sales: 12.619606<br />facebook: #3366FF","youtube: 63.723038<br />sales: 12.879426<br />facebook: #3366FF","youtube: 68.214684<br />sales: 13.139246<br />facebook: #3366FF","youtube: 72.706329<br />sales: 13.399065<br />facebook: #3366FF","youtube: 77.197975<br />sales: 13.658885<br />facebook: #3366FF","youtube: 81.689620<br />sales: 13.918705<br />facebook: #3366FF","youtube: 86.181266<br />sales: 14.178524<br />facebook: #3366FF","youtube: 90.672911<br />sales: 14.438344<br />facebook: #3366FF","youtube: 95.164557<br />sales: 14.698164<br />facebook: #3366FF","youtube: 99.656203<br />sales: 14.957984<br />facebook: #3366FF","youtube: 104.147848<br />sales: 15.217803<br />facebook: #3366FF","youtube: 108.639494<br />sales: 15.477623<br />facebook: #3366FF","youtube: 113.131139<br />sales: 15.737443<br />facebook: #3366FF","youtube: 117.622785<br />sales: 15.997262<br />facebook: #3366FF","youtube: 122.114430<br />sales: 16.257082<br />facebook: #3366FF","youtube: 126.606076<br />sales: 16.516902<br />facebook: #3366FF","youtube: 131.097722<br />sales: 16.776722<br />facebook: #3366FF","youtube: 135.589367<br />sales: 17.036541<br />facebook: #3366FF","youtube: 140.081013<br />sales: 17.296361<br />facebook: #3366FF","youtube: 144.572658<br />sales: 17.556181<br />facebook: #3366FF","youtube: 149.064304<br />sales: 17.816000<br />facebook: #3366FF","youtube: 153.555949<br />sales: 18.075820<br />facebook: #3366FF","youtube: 158.047595<br />sales: 18.335640<br />facebook: #3366FF","youtube: 162.539241<br />sales: 18.595460<br />facebook: #3366FF","youtube: 167.030886<br />sales: 18.855279<br />facebook: #3366FF","youtube: 171.522532<br />sales: 19.115099<br />facebook: #3366FF","youtube: 176.014177<br />sales: 19.374919<br />facebook: #3366FF","youtube: 180.505823<br />sales: 19.634738<br />facebook: #3366FF","youtube: 184.997468<br />sales: 19.894558<br />facebook: #3366FF","youtube: 189.489114<br />sales: 20.154378<br />facebook: #3366FF","youtube: 193.980759<br />sales: 20.414197<br />facebook: #3366FF","youtube: 198.472405<br />sales: 20.674017<br />facebook: #3366FF","youtube: 202.964051<br />sales: 20.933837<br />facebook: #3366FF","youtube: 207.455696<br />sales: 21.193657<br />facebook: #3366FF","youtube: 211.947342<br />sales: 21.453476<br />facebook: #3366FF","youtube: 216.438987<br />sales: 21.713296<br />facebook: #3366FF","youtube: 220.930633<br />sales: 21.973116<br />facebook: #3366FF","youtube: 225.422278<br />sales: 22.232935<br />facebook: #3366FF","youtube: 229.913924<br />sales: 22.492755<br />facebook: #3366FF","youtube: 234.405570<br />sales: 22.752575<br />facebook: #3366FF","youtube: 238.897215<br />sales: 23.012395<br />facebook: #3366FF","youtube: 243.388861<br />sales: 23.272214<br />facebook: #3366FF","youtube: 247.880506<br />sales: 23.532034<br />facebook: #3366FF","youtube: 252.372152<br />sales: 23.791854<br />facebook: #3366FF","youtube: 256.863797<br />sales: 24.051673<br />facebook: #3366FF","youtube: 261.355443<br />sales: 24.311493<br />facebook: #3366FF","youtube: 265.847089<br />sales: 24.571313<br />facebook: #3366FF","youtube: 270.338734<br />sales: 24.831133<br />facebook: #3366FF","youtube: 274.830380<br />sales: 25.090952<br />facebook: #3366FF","youtube: 279.322025<br />sales: 25.350772<br />facebook: #3366FF","youtube: 283.813671<br />sales: 25.610592<br />facebook: #3366FF","youtube: 288.305316<br />sales: 25.870411<br />facebook: #3366FF","youtube: 292.796962<br />sales: 26.130231<br />facebook: #3366FF","youtube: 297.288608<br />sales: 26.390051<br />facebook: #3366FF","youtube: 301.780253<br />sales: 26.649871<br />facebook: #3366FF","youtube: 306.271899<br />sales: 26.909690<br />facebook: #3366FF","youtube: 310.763544<br />sales: 27.169510<br />facebook: #3366FF","youtube: 315.255190<br />sales: 27.429330<br />facebook: #3366FF","youtube: 319.746835<br />sales: 27.689149<br />facebook: #3366FF","youtube: 324.238481<br />sales: 27.948969<br />facebook: #3366FF","youtube: 328.730127<br />sales: 28.208789<br />facebook: #3366FF","youtube: 333.221772<br />sales: 28.468609<br />facebook: #3366FF","youtube: 337.713418<br />sales: 28.728428<br />facebook: #3366FF","youtube: 342.205063<br />sales: 28.988248<br />facebook: #3366FF","youtube: 346.696709<br />sales: 29.248068<br />facebook: #3366FF","youtube: 351.188354<br />sales: 29.507887<br />facebook: #3366FF","youtube: 355.680000<br />sales: 29.767707<br />facebook: #3366FF"],"type":"scatter","mode":"lines","name":"fitted values","line":{"width":3.77952755905512,"color":"rgba(51,102,255,1)","dash":"solid"},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[4.92,9.27341772151899,13.626835443038,17.980253164557,22.3336708860759,26.6870886075949,31.0405063291139,35.3939240506329,39.7473417721519,44.1007594936709,48.4541772151899,52.8075949367089,57.1610126582278,61.5144303797468,65.8678481012658,70.2212658227848,74.5746835443038,78.9281012658228,83.2815189873418,87.6349367088608,91.9883544303797,96.3417721518987,100.695189873418,105.048607594937,109.402025316456,113.755443037975,118.108860759494,122.462278481013,126.815696202532,131.169113924051,135.52253164557,139.875949367089,144.229367088608,148.582784810127,152.936202531646,157.289620253165,161.643037974684,165.996455696203,170.349873417722,174.70329113924,179.056708860759,183.410126582278,187.763544303797,192.116962025316,196.470379746835,200.823797468354,205.177215189873,209.530632911392,213.884050632911,218.23746835443,222.590886075949,226.944303797468,231.297721518987,235.651139240506,240.004556962025,244.357974683544,248.711392405063,253.064810126582,257.418227848101,261.77164556962,266.125063291139,270.478481012658,274.831898734177,279.185316455696,283.538734177215,287.892151898734,292.245569620253,296.598987341772,300.952405063291,305.30582278481,309.659240506329,314.012658227848,318.366075949367,322.719493670886,327.072911392405,331.426329113924,335.779746835443,340.133164556962,344.486582278481,348.84],"y":[8.73403439224642,8.85895527843762,8.98387616462882,9.10879705082002,9.23371793701122,9.35863882320242,9.48355970939361,9.60848059558481,9.73340148177601,9.85832236796721,9.98324325415841,10.1081641403496,10.2330850265408,10.358005912732,10.4829267989232,10.6078476851144,10.7327685713056,10.8576894574968,10.982610343688,11.1075312298792,11.2324521160704,11.3573730022616,11.4822938884528,11.607214774644,11.7321356608352,11.8570565470264,11.9819774332176,12.1068983194088,12.2318192056,12.3567400917912,12.4816609779824,12.6065818641736,12.7315027503648,12.856423636556,12.9813445227472,13.1062654089384,13.2311862951296,13.3561071813208,13.481028067512,13.6059489537032,13.7308698398944,13.8557907260855,13.9807116122767,14.1056324984679,14.2305533846591,14.3554742708503,14.4803951570415,14.6053160432327,14.7302369294239,14.8551578156151,14.9800787018063,15.1049995879975,15.2299204741887,15.3548413603799,15.4797622465711,15.6046831327623,15.7296040189535,15.8545249051447,15.9794457913359,16.1043666775271,16.2292875637183,16.3542084499095,16.4791293361007,16.6040502222919,16.7289711084831,16.8538919946743,16.9788128808655,17.1037337670567,17.2286546532479,17.3535755394391,17.4784964256303,17.6034173118215,17.7283381980127,17.8532590842039,17.9781799703951,18.1031008565863,18.2280217427775,18.3529426289687,18.4778635151599,18.6027844013511],"text":["youtube: 4.920000<br />sales: 8.734034<br />facebook: #3366FF","youtube: 9.273418<br />sales: 8.858955<br />facebook: #3366FF","youtube: 13.626835<br />sales: 8.983876<br />facebook: #3366FF","youtube: 17.980253<br />sales: 9.108797<br />facebook: #3366FF","youtube: 22.333671<br />sales: 9.233718<br />facebook: #3366FF","youtube: 26.687089<br />sales: 9.358639<br />facebook: #3366FF","youtube: 31.040506<br />sales: 9.483560<br />facebook: #3366FF","youtube: 35.393924<br />sales: 9.608481<br />facebook: #3366FF","youtube: 39.747342<br />sales: 9.733401<br />facebook: #3366FF","youtube: 44.100759<br />sales: 9.858322<br />facebook: #3366FF","youtube: 48.454177<br />sales: 9.983243<br />facebook: #3366FF","youtube: 52.807595<br />sales: 10.108164<br />facebook: #3366FF","youtube: 57.161013<br />sales: 10.233085<br />facebook: #3366FF","youtube: 61.514430<br />sales: 10.358006<br />facebook: #3366FF","youtube: 65.867848<br />sales: 10.482927<br />facebook: #3366FF","youtube: 70.221266<br />sales: 10.607848<br />facebook: #3366FF","youtube: 74.574684<br />sales: 10.732769<br />facebook: #3366FF","youtube: 78.928101<br />sales: 10.857689<br />facebook: #3366FF","youtube: 83.281519<br />sales: 10.982610<br />facebook: #3366FF","youtube: 87.634937<br />sales: 11.107531<br />facebook: #3366FF","youtube: 91.988354<br />sales: 11.232452<br />facebook: #3366FF","youtube: 96.341772<br />sales: 11.357373<br />facebook: #3366FF","youtube: 100.695190<br />sales: 11.482294<br />facebook: #3366FF","youtube: 105.048608<br />sales: 11.607215<br />facebook: #3366FF","youtube: 109.402025<br />sales: 11.732136<br />facebook: #3366FF","youtube: 113.755443<br />sales: 11.857057<br />facebook: #3366FF","youtube: 118.108861<br />sales: 11.981977<br />facebook: #3366FF","youtube: 122.462278<br />sales: 12.106898<br />facebook: #3366FF","youtube: 126.815696<br />sales: 12.231819<br />facebook: #3366FF","youtube: 131.169114<br />sales: 12.356740<br />facebook: #3366FF","youtube: 135.522532<br />sales: 12.481661<br />facebook: #3366FF","youtube: 139.875949<br />sales: 12.606582<br />facebook: #3366FF","youtube: 144.229367<br />sales: 12.731503<br />facebook: #3366FF","youtube: 148.582785<br />sales: 12.856424<br />facebook: #3366FF","youtube: 152.936203<br />sales: 12.981345<br />facebook: #3366FF","youtube: 157.289620<br />sales: 13.106265<br />facebook: #3366FF","youtube: 161.643038<br />sales: 13.231186<br />facebook: #3366FF","youtube: 165.996456<br />sales: 13.356107<br />facebook: #3366FF","youtube: 170.349873<br />sales: 13.481028<br />facebook: #3366FF","youtube: 174.703291<br />sales: 13.605949<br />facebook: #3366FF","youtube: 179.056709<br />sales: 13.730870<br />facebook: #3366FF","youtube: 183.410127<br />sales: 13.855791<br />facebook: #3366FF","youtube: 187.763544<br />sales: 13.980712<br />facebook: #3366FF","youtube: 192.116962<br />sales: 14.105632<br />facebook: #3366FF","youtube: 196.470380<br />sales: 14.230553<br />facebook: #3366FF","youtube: 200.823797<br />sales: 14.355474<br />facebook: #3366FF","youtube: 205.177215<br />sales: 14.480395<br />facebook: #3366FF","youtube: 209.530633<br />sales: 14.605316<br />facebook: #3366FF","youtube: 213.884051<br />sales: 14.730237<br />facebook: #3366FF","youtube: 218.237468<br />sales: 14.855158<br />facebook: #3366FF","youtube: 222.590886<br />sales: 14.980079<br />facebook: #3366FF","youtube: 226.944304<br />sales: 15.105000<br />facebook: #3366FF","youtube: 231.297722<br />sales: 15.229920<br />facebook: #3366FF","youtube: 235.651139<br />sales: 15.354841<br />facebook: #3366FF","youtube: 240.004557<br />sales: 15.479762<br />facebook: #3366FF","youtube: 244.357975<br />sales: 15.604683<br />facebook: #3366FF","youtube: 248.711392<br />sales: 15.729604<br />facebook: #3366FF","youtube: 253.064810<br />sales: 15.854525<br />facebook: #3366FF","youtube: 257.418228<br />sales: 15.979446<br />facebook: #3366FF","youtube: 261.771646<br />sales: 16.104367<br />facebook: #3366FF","youtube: 266.125063<br />sales: 16.229288<br />facebook: #3366FF","youtube: 270.478481<br />sales: 16.354208<br />facebook: #3366FF","youtube: 274.831899<br />sales: 16.479129<br />facebook: #3366FF","youtube: 279.185316<br />sales: 16.604050<br />facebook: #3366FF","youtube: 283.538734<br />sales: 16.728971<br />facebook: #3366FF","youtube: 287.892152<br />sales: 16.853892<br />facebook: #3366FF","youtube: 292.245570<br />sales: 16.978813<br />facebook: #3366FF","youtube: 296.598987<br />sales: 17.103734<br />facebook: #3366FF","youtube: 300.952405<br />sales: 17.228655<br />facebook: #3366FF","youtube: 305.305823<br />sales: 17.353576<br />facebook: #3366FF","youtube: 309.659241<br />sales: 17.478496<br />facebook: #3366FF","youtube: 314.012658<br />sales: 17.603417<br />facebook: #3366FF","youtube: 318.366076<br />sales: 17.728338<br />facebook: #3366FF","youtube: 322.719494<br />sales: 17.853259<br />facebook: #3366FF","youtube: 327.072911<br />sales: 17.978180<br />facebook: #3366FF","youtube: 331.426329<br />sales: 18.103101<br />facebook: #3366FF","youtube: 335.779747<br />sales: 18.228022<br />facebook: #3366FF","youtube: 340.133165<br />sales: 18.352943<br />facebook: #3366FF","youtube: 344.486582<br />sales: 18.477864<br />facebook: #3366FF","youtube: 348.840000<br />sales: 18.602784<br />facebook: #3366FF"],"type":"scatter","mode":"lines","name":"fitted values","line":{"width":3.77952755905512,"color":"rgba(51,102,255,1)","dash":"solid"},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[0],"y":[10],"name":"99_426a7f45792e58d5d7ffa141cbc0216e","type":"scatter","mode":"markers","opacity":0,"hoverinfo":"skip","showlegend":false,"marker":{"color":[0,1],"colorscale":[[0,"#132B43"],[0.00334448160535117,"#132B44"],[0.00668896321070234,"#132C44"],[0.0100334448160535,"#142C45"],[0.0133779264214047,"#142D45"],[0.0167224080267559,"#142D46"],[0.020066889632107,"#142D46"],[0.0234113712374582,"#142E47"],[0.0267558528428094,"#152E47"],[0.0301003344481605,"#152F48"],[0.0334448160535117,"#152F48"],[0.0367892976588629,"#152F49"],[0.040133779264214,"#153049"],[0.0434782608695652,"#16304A"],[0.0468227424749164,"#16304A"],[0.0501672240802676,"#16314B"],[0.0535117056856187,"#16314B"],[0.0568561872909699,"#16324C"],[0.0602006688963211,"#17324D"],[0.0635451505016722,"#17324D"],[0.0668896321070234,"#17334E"],[0.0702341137123746,"#17334E"],[0.0735785953177257,"#17344F"],[0.0769230769230769,"#18344F"],[0.0802675585284281,"#183450"],[0.0836120401337793,"#183550"],[0.0869565217391304,"#183551"],[0.0903010033444816,"#183651"],[0.0936454849498328,"#193652"],[0.0969899665551839,"#193652"],[0.100334448160535,"#193753"],[0.103678929765886,"#193754"],[0.107023411371237,"#193854"],[0.110367892976589,"#1A3855"],[0.11371237458194,"#1A3955"],[0.117056856187291,"#1A3956"],[0.120401337792642,"#1A3956"],[0.123745819397993,"#1A3A57"],[0.127090301003344,"#1B3A57"],[0.130434782608696,"#1B3B58"],[0.133779264214047,"#1B3B59"],[0.137123745819398,"#1B3B59"],[0.140468227424749,"#1C3C5A"],[0.1438127090301,"#1C3C5A"],[0.147157190635451,"#1C3D5B"],[0.150501672240803,"#1C3D5B"],[0.153846153846154,"#1C3D5C"],[0.157190635451505,"#1D3E5C"],[0.160535117056856,"#1D3E5D"],[0.163879598662207,"#1D3F5D"],[0.167224080267559,"#1D3F5E"],[0.17056856187291,"#1D3F5F"],[0.173913043478261,"#1E405F"],[0.177257525083612,"#1E4060"],[0.180602006688963,"#1E4160"],[0.183946488294314,"#1E4161"],[0.187290969899666,"#1E4261"],[0.190635451505017,"#1F4262"],[0.193979933110368,"#1F4263"],[0.197324414715719,"#1F4363"],[0.20066889632107,"#1F4364"],[0.204013377926421,"#1F4464"],[0.207357859531773,"#204465"],[0.210702341137124,"#204465"],[0.214046822742475,"#204566"],[0.217391304347826,"#204566"],[0.220735785953177,"#214667"],[0.224080267558528,"#214668"],[0.22742474916388,"#214768"],[0.230769230769231,"#214769"],[0.234113712374582,"#214769"],[0.237458193979933,"#22486A"],[0.240802675585284,"#22486A"],[0.244147157190635,"#22496B"],[0.247491638795987,"#22496C"],[0.250836120401338,"#224A6C"],[0.254180602006689,"#234A6D"],[0.25752508361204,"#234A6D"],[0.260869565217391,"#234B6E"],[0.264214046822742,"#234B6E"],[0.267558528428094,"#244C6F"],[0.270903010033445,"#244C70"],[0.274247491638796,"#244C70"],[0.277591973244147,"#244D71"],[0.280936454849498,"#244D71"],[0.284280936454849,"#254E72"],[0.287625418060201,"#254E72"],[0.290969899665552,"#254F73"],[0.294314381270903,"#254F74"],[0.297658862876254,"#254F74"],[0.301003344481605,"#265075"],[0.304347826086956,"#265075"],[0.307692307692308,"#265176"],[0.311036789297659,"#265176"],[0.31438127090301,"#275277"],[0.317725752508361,"#275278"],[0.321070234113712,"#275278"],[0.324414715719064,"#275379"],[0.327759197324415,"#275379"],[0.331103678929766,"#28547A"],[0.334448160535117,"#28547B"],[0.337792642140468,"#28557B"],[0.341137123745819,"#28557C"],[0.344481605351171,"#28567C"],[0.347826086956522,"#29567D"],[0.351170568561873,"#29567D"],[0.354515050167224,"#29577E"],[0.357859531772575,"#29577F"],[0.361204013377926,"#2A587F"],[0.364548494983278,"#2A5880"],[0.367892976588629,"#2A5980"],[0.37123745819398,"#2A5981"],[0.374581939799331,"#2A5982"],[0.377926421404682,"#2B5A82"],[0.381270903010033,"#2B5A83"],[0.384615384615385,"#2B5B83"],[0.387959866220736,"#2B5B84"],[0.391304347826087,"#2C5C85"],[0.394648829431438,"#2C5C85"],[0.397993311036789,"#2C5D86"],[0.40133779264214,"#2C5D86"],[0.404682274247492,"#2C5D87"],[0.408026755852843,"#2D5E87"],[0.411371237458194,"#2D5E88"],[0.414715719063545,"#2D5F89"],[0.418060200668896,"#2D5F89"],[0.421404682274247,"#2E608A"],[0.424749163879599,"#2E608A"],[0.42809364548495,"#2E618B"],[0.431438127090301,"#2E618C"],[0.434782608695652,"#2E618C"],[0.438127090301003,"#2F628D"],[0.441471571906354,"#2F628D"],[0.444816053511706,"#2F638E"],[0.448160535117057,"#2F638F"],[0.451505016722408,"#30648F"],[0.454849498327759,"#306490"],[0.45819397993311,"#306590"],[0.461538461538462,"#306591"],[0.464882943143813,"#306592"],[0.468227424749164,"#316692"],[0.471571906354515,"#316693"],[0.474916387959866,"#316793"],[0.478260869565217,"#316794"],[0.481605351170569,"#326895"],[0.48494983277592,"#326895"],[0.488294314381271,"#326996"],[0.491638795986622,"#326996"],[0.494983277591973,"#326997"],[0.498327759197324,"#336A98"],[0.501672240802676,"#336A98"],[0.505016722408027,"#336B99"],[0.508361204013378,"#336B99"],[0.511705685618729,"#346C9A"],[0.51505016722408,"#346C9B"],[0.518394648829431,"#346D9B"],[0.521739130434783,"#346D9C"],[0.525083612040134,"#346E9D"],[0.528428093645485,"#356E9D"],[0.531772575250836,"#356E9E"],[0.535117056856187,"#356F9E"],[0.538461538461538,"#356F9F"],[0.54180602006689,"#3670A0"],[0.545150501672241,"#3670A0"],[0.548494983277592,"#3671A1"],[0.551839464882943,"#3671A1"],[0.555183946488294,"#3772A2"],[0.558528428093645,"#3772A3"],[0.561872909698997,"#3773A3"],[0.565217391304348,"#3773A4"],[0.568561872909699,"#3773A4"],[0.57190635451505,"#3874A5"],[0.575250836120401,"#3874A6"],[0.578595317725752,"#3875A6"],[0.581939799331104,"#3875A7"],[0.585284280936455,"#3976A8"],[0.588628762541806,"#3976A8"],[0.591973244147157,"#3977A9"],[0.595317725752508,"#3977A9"],[0.598662207357859,"#3978AA"],[0.602006688963211,"#3A78AB"],[0.605351170568562,"#3A79AB"],[0.608695652173913,"#3A79AC"],[0.612040133779264,"#3A79AC"],[0.615384615384615,"#3B7AAD"],[0.618729096989967,"#3B7AAE"],[0.622073578595318,"#3B7BAE"],[0.625418060200669,"#3B7BAF"],[0.62876254180602,"#3C7CB0"],[0.632107023411371,"#3C7CB0"],[0.635451505016722,"#3C7DB1"],[0.638795986622074,"#3C7DB1"],[0.642140468227425,"#3C7EB2"],[0.645484949832776,"#3D7EB3"],[0.648829431438127,"#3D7FB3"],[0.652173913043478,"#3D7FB4"],[0.655518394648829,"#3D7FB5"],[0.658862876254181,"#3E80B5"],[0.662207357859532,"#3E80B6"],[0.665551839464883,"#3E81B6"],[0.668896321070234,"#3E81B7"],[0.672240802675585,"#3F82B8"],[0.675585284280936,"#3F82B8"],[0.678929765886288,"#3F83B9"],[0.682274247491639,"#3F83BA"],[0.68561872909699,"#4084BA"],[0.688963210702341,"#4084BB"],[0.692307692307692,"#4085BB"],[0.695652173913043,"#4085BC"],[0.698996655518395,"#4086BD"],[0.702341137123746,"#4186BD"],[0.705685618729097,"#4186BE"],[0.709030100334448,"#4187BF"],[0.712374581939799,"#4187BF"],[0.71571906354515,"#4288C0"],[0.719063545150502,"#4288C1"],[0.722408026755853,"#4289C1"],[0.725752508361204,"#4289C2"],[0.729096989966555,"#438AC2"],[0.732441471571906,"#438AC3"],[0.735785953177257,"#438BC4"],[0.739130434782609,"#438BC4"],[0.74247491638796,"#438CC5"],[0.745819397993311,"#448CC6"],[0.749163879598662,"#448DC6"],[0.752508361204013,"#448DC7"],[0.755852842809364,"#448EC8"],[0.759197324414716,"#458EC8"],[0.762541806020067,"#458FC9"],[0.765886287625418,"#458FC9"],[0.769230769230769,"#458FCA"],[0.77257525083612,"#4690CB"],[0.775919732441471,"#4690CB"],[0.779264214046823,"#4691CC"],[0.782608695652174,"#4691CD"],[0.785953177257525,"#4792CD"],[0.789297658862876,"#4792CE"],[0.792642140468227,"#4793CF"],[0.795986622073579,"#4793CF"],[0.79933110367893,"#4894D0"],[0.802675585284281,"#4894D0"],[0.806020066889632,"#4895D1"],[0.809364548494983,"#4895D2"],[0.812709030100334,"#4896D2"],[0.816053511705686,"#4996D3"],[0.819397993311037,"#4997D4"],[0.822742474916388,"#4997D4"],[0.826086956521739,"#4998D5"],[0.82943143812709,"#4A98D6"],[0.832775919732441,"#4A99D6"],[0.836120401337793,"#4A99D7"],[0.839464882943144,"#4A9AD8"],[0.842809364548495,"#4B9AD8"],[0.846153846153846,"#4B9BD9"],[0.849498327759197,"#4B9BDA"],[0.852842809364548,"#4B9BDA"],[0.8561872909699,"#4C9CDB"],[0.859531772575251,"#4C9CDB"],[0.862876254180602,"#4C9DDC"],[0.866220735785953,"#4C9DDD"],[0.869565217391304,"#4D9EDD"],[0.872909698996655,"#4D9EDE"],[0.876254180602007,"#4D9FDF"],[0.879598662207358,"#4D9FDF"],[0.882943143812709,"#4DA0E0"],[0.88628762541806,"#4EA0E1"],[0.889632107023411,"#4EA1E1"],[0.892976588628762,"#4EA1E2"],[0.896321070234114,"#4EA2E3"],[0.899665551839465,"#4FA2E3"],[0.903010033444816,"#4FA3E4"],[0.906354515050167,"#4FA3E5"],[0.909698996655518,"#4FA4E5"],[0.91304347826087,"#50A4E6"],[0.916387959866221,"#50A5E7"],[0.919732441471572,"#50A5E7"],[0.923076923076923,"#50A6E8"],[0.926421404682274,"#51A6E8"],[0.929765886287625,"#51A7E9"],[0.933110367892977,"#51A7EA"],[0.936454849498328,"#51A8EA"],[0.939799331103679,"#52A8EB"],[0.94314381270903,"#52A9EC"],[0.946488294314381,"#52A9EC"],[0.949832775919732,"#52AAED"],[0.953177257525084,"#53AAEE"],[0.956521739130435,"#53ABEE"],[0.959866220735786,"#53ABEF"],[0.963210702341137,"#53ACF0"],[0.966555183946488,"#54ACF0"],[0.969899665551839,"#54ADF1"],[0.973244147157191,"#54ADF2"],[0.976588628762542,"#54AEF2"],[0.979933110367893,"#55AEF3"],[0.983277591973244,"#55AFF4"],[0.986622073578595,"#55AFF4"],[0.989966555183946,"#55B0F5"],[0.993311036789298,"#56B0F6"],[0.996655518394649,"#56B1F6"],[1,"#56B1F7"]],"colorbar":{"bgcolor":null,"bordercolor":null,"borderwidth":0,"thickness":23.04,"title":"facebook","titlefont":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187},"tickmode":"array","ticktext":["0","10","20","30","40","50"],"tickvals":[0,0.168010752688172,0.336021505376344,0.504032258064516,0.672043010752688,0.84005376344086],"tickfont":{"color":"rgba(0,0,0,1)","family":"","size":11.689497716895},"ticklen":2,"len":0.5}},"xaxis":"x","yaxis":"y","frame":null}],"layout":{"margin":{"t":28.1765601217656,"r":7.30593607305936,"b":42.130898021309,"l":37.2602739726027},"font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187},"xaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[-16.902,373.422],"tickmode":"array","ticktext":["0","100","200","300"],"tickvals":[0,100,200,300],"categoryorder":"array","categoryarray":["0","100","200","300"],"nticks":null,"ticks":"","tickcolor":null,"ticklen":3.65296803652968,"tickwidth":0,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.689497716895},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176,"zeroline":false,"anchor":"y","title":{"text":"youtube","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"yaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[0.396,33.924],"tickmode":"array","ticktext":["10","20","30"],"tickvals":[10,20,30],"categoryorder":"array","categoryarray":["10","20","30"],"nticks":null,"ticks":"","tickcolor":null,"ticklen":3.65296803652968,"tickwidth":0,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.689497716895},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176,"zeroline":false,"anchor":"x","title":{"text":"sales","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"shapes":[{"type":"rect","fillcolor":null,"line":{"color":null,"width":0,"linetype":[]},"yref":"paper","xref":"paper","x0":0,"x1":1,"y0":0,"y1":1}],"showlegend":false,"legend":{"bgcolor":null,"bordercolor":null,"borderwidth":0,"font":{"color":"rgba(0,0,0,1)","family":"","size":11.689497716895}},"hovermode":"closest","barmode":"relative"},"config":{"doubleClick":"reset","showSendToCloud":false},"source":"A","attrs":{"1ecf6110840a":{"x":{},"y":{},"colour":{},"type":"scatter"},"1ecf34cde4f":{"x":{},"y":{},"colour":{}},"1ecf2b97163a":{"x":{},"y":{},"colour":{}}},"cur_data":"1ecf6110840a","visdat":{"1ecf6110840a":["function (y) ","x"],"1ecf34cde4f":["function (y) ","x"],"1ecf2b97163a":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.2,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- ## Contact Tong Jin - Email: tj1061@nyu.edu - Office Hours - Mondays, 9 - 10am (EST) - Wednesdays, 12:30 - 1:30pm (EST)